In a standard card deck, there are 52 different cards, which are divided into 4 suits (spades, diamonds, clubs, and hearts), with each suit containing 13 cards. What is the probability that in a randomly selected rearrangement of the card deck, the 3 of spades is after all the hearts

Answers

Answer 1

In a given permutation of 52 cards, if the 3 of spades is to follow all of the hearts, that means the 3 of spades must be at least the 14th card in the deck.

Consider some possible orderings of the deck:

• If the 3 of spades is the 14th card, then the deck looks like

[all 13 ♥] … 3 ♠ … [all other 38 cards]

There are 13! ways to arrange the 13 hearts at the beginning and 38! ways to arrange the tail of 38 cards. Hence there are 13! × 38! possible rearrangements of the deck where 3 ♠ is the 14th card.

• If 3 ♠ is the 15th card, then the deck looks like

[13 ♥ and 1 other] … 3 ♠ … [all other 37 cards]

and there would be 14! × 37! ways of arranging the cards in this order.

There are 39 possible positions for 3 ♠. Extrapolating, it follows that the total number of permutations of the deck in which all hearts occur before 3 ♠ is

[tex]\displaystyle \sum_{k=0}^{38} (13+k)! \times (38-k)![/tex]

There are 52! total possible ways of rearranging the deck. Then the probability of rearranging the deck so that all hearts are drawn before 3 ♠ is

[tex]\displaystyle \frac1{52!} \sum_{k=0}^{38} (13+k)! \times (38-k)! = \frac{87,031,512,096,420,449}{221,360,321,731,856,907,600} \approx \boxed{0.000393}[/tex]


Related Questions

You kayak up a river at a rate of 28 feet every 30 seconds. You kayak 423 feet every 9 minutes on the way back down the river. How fast are you traveling up river? down river? (Be sure and change your seconds to minutes)

Up River:
ft:
min

Down River:
ft:
min

Answers

You traveled up the river at 56 feet a minute and down the river at 47 feet a minute.

The question is asking us to simply convert the speed traveled in feet per second to feet per minute. To do that, we say,

28 feet in 30 seconds, if we multiply both by two. We have 56 feet in 60 seconds. Also remember that 60 seconds make 1 minute. Thus, you must have kayaked up the river at 56 feet in a minute.

423 feet in 9 minutes, if we divide both by nine. We have 47 feet in a minute. This means that you kayaked 47 feet a minute down the river.

for more visit https://brainly.com/question/25552839

Is 100 a reasonable estimate for 915.25 +88.22? Explain.​

Answers

Answer:

When estimating always round to the nearest whole number, 10th or 100th.

Im not sure if which estimation you are requesting in this question but i'l give you three answers:

The nearest whole number which would be 915 and 88 would be 1,003

The nearest 10th which is 920 and 90 which would be 1,010

The nearest 100th which would be 900 and 90 which would be 990

What series of transformation will not map figure H onto itself

Answers

Answer:

D

Step-by-step explanation:  

Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2)

Consider option D.

1st transformation  will map vertices of the square into points

....2nd transformation = reflection over y = -x + 2 will map vertices into points ....

These points are not the vertices of the initial square.

I hope it helps.

Find the missing side.
09
9.5
10
C
7 cm
10.6
8 cm
HELP PLEASE

Answers

Answer:a

Step-by-step explanation:

i know

Jada, Elena, Lin walked a total of 37 miles last week. Jada walke 4 miles in Elena, and Lin walked 2 more miles than Jada.
Click on picture for more info :333









I AM BEING NICE TODAY. DONT I REPEAT DONT TAKE THE POINTS AND ANSWER A NONSENSICAL ANSWER. THIS WILL END UP IN AN REPORT LIKE BIG TIME >:<
I AM GIVING 100 POINTS AND BRAINLIEST. PRIZE GOES TO ONE WHO ANSWER FIRST AND CORRECTLY.

Answers

Elena walked=mJada walked=m+4Lin walked=m+6

ATQ

[tex]\\ \sf\longmapsto m+m+4+m+6=37[/tex]

[tex]\\ \sf\longmapsto 3m+10=37[/tex]

[tex]\\ \sf\longmapsto 3m=27[/tex]

[tex]\\ \sf\longmapsto m=9[/tex]

Elena=9miJade=13miLin=15mi

What is the y intersect. Pls help

Answers

Answer:

total shipping cost

Step-by-step explanation:

PLEASE HELP ME WILL GIVE BRAINLIEST!!!!!
How do you graph the solution set to a system of linear inequalities in two variables (pretend you are the teacher and you are teaching me how to graph it)?

Answers

Answer:

Graph both of the line inequalities on the same coordinate graph, and then the overlap will be your answer.

Step-by-step explanation:

An example is attached! The purple-ish on the right would be your solution set.

John earned $12 a day for babysitting his siblings after school each weekday (he did not babysit on weekends). He liked to have a small amount of money to spend on treats at the school canteen that his parents refuse to buy, but he also wanted to build up some savings. John decided to put a fraction of his earnings into a jar straight away. He spent all the rest on canteen treats.


How much money did John earn over a nine week term?

After 9 weeks, John had $378 in his jar. What percentage of his money did he save?

Answers

Answer:

He earns $540

70% of his money went to savings

Step-by-step explanation:

9 weeks x 5 days a week = 45 days

45 days x $12 a day = $540

378 * 100 / 540 =  (378*100) / 540 =  37800/540 = %70

What are the coordinates of point P?



O (-4, 3)
O (-3, 4)
0 (3,-4)
O (4, -3)

Answers

The answer will have to end up being(-4,3) that’s all I just need more words for whatever reason

Answer:

(-4, 3)

Step-by-step explanation:

You have to go -4 on the x-axis, and +3 on the y-axis

(4)/(12)= ()/(3) what makes this equivalent

Answers

Answer:

1/3

Step-by-step explanation:

4/12 divide by 4 to the top and bottom you get 1/3

[tex]\dfrac 4{12} = \dfrac{ 4 \times \tfrac 14 }{12 \times \tfrac 14} = \dfrac 13\\\\\\\\\text{Hence the answer is 1}[/tex]

[tex]\sqrt{17} \times \sqrt{17}[/tex]

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The equivalent value is ~

[tex] \boxed{17}[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

[tex] \sqrt{17} \times \sqrt{17} [/tex]

[tex]( \sqrt{17}) {}^{2} [/tex]

[tex]{(17 {}^{ \frac{1}{2}}) }^{2} [/tex]

[tex]17[/tex]

5^-15 rewritten using a positive exponent.

Answers

Answer: 1/5 to the power of 15

How to synthetically divide polynomials.

Answers

Answer:

Write down the problem. For this example, you will be dividing x3 + 2x2 - 4x + 8 by x + 2. Write the first polynomial equation, the dividend, in the numerator and write the second equation, the divisor, in the denominator.

Reverse the sign of the constant in the divisor. The constant in the divisor, x + 2, is positive 2, so reversing the sign of the constant would give you -2.

Since the opposite of the constant term is -2, we put the -2 inside a box. A common mistake is to put a 2 inside the box, watch out here.

Write all of the coefficients of the dividend inside the division symbol. [2] Write the terms from left to right, just as they appear. It should look like this: -2| 1 2 -4 8.

Bring down the first coefficient. Bring down the first coefficient, 1, below itself. It should look like this:

-2| 1  2  -4  8

   ↓

   1

Multiply the first coefficient by the divisor and place it under the second coefficient.[3] Simply multiply 1 by -2 to get -2 and write this product under the second term, 2. Here's how it would look:

-2| 1  2  -4  8

       -2

   1

Add the second coefficient and the product and write the answer below the product. Now take the second coefficient, 2, and add it to -2. The result is 0. Write this result below the two numbers, just as you would in long division. Here's how it would look:

-2| 1  2  -4  8

       -2

   1   0

Multiply this sum by the divisor and place the result under the third coefficient. Now take the sum, 0, and multiply it by the divisor, -2. The result is 0. Place this number below 4, the third coefficient. It should look like this:

-2| 1  2  -4  8

       -2  0  

   1  

Add the product and the third coefficient and write the result under the product. Add 0 and -4 to get -4 and write this answer below the 0. Here's how it would look:

-2| 1  2  -4  8

       -2   0  

   1   0   -4

Multiply this number by the divisor, write it under the last coefficient, and add it to the coefficient. Now, multiply -4 by -2 to get 8, write this answer under the fourth coefficient, 8, and add this answer to the fourth coefficient. 8 + 8 = 16, so this is your remainder. Write this number below the product. Here's how it would look:

-2| 1  2  -4  8

       -2   0   8

   1   0   -4   |16

Place each of the new coefficients next to a variable of one less power than their original corresponding variables. In this case, the first sum, 1, is placed next to an x to the second power (one less than three). The second sum, 0, is placed next to an x, but the result is zero, so you can remove this term. And the third coefficient, -4, becomes a constant, a number without a variable, since the original variable was x. You can write an R next to the 16, because that is the remainder. Here's how it would look:

-2| 1  2  -4  8

       -2   0   8

   1   0   -4   |16

   x2   + 0x    - 4    R 16

x2 - 4 R16

Write the final answer. The final answer is the new polynomial, x2 - 4, plus the remainder, 16, over the original divisor, x + 2. Here's how it would look: x2 - 4 +16/(x +2).

Step-by-step explanation:

That was quite long, but those are the steps to synthetically divide polynomials.

Tommy and his friend went to go buy pie at Delicious Orchards. After paying seven dollars for the pie, Tommy
has ninety-five dollars left, his friend has forty dollars. How much money did Tommy have before buying the
ple.

Answers

Answer:

$102

Step-by-step explanation:

if Tommy spent 7 dollars on pie, that means he had more money than that amount before.

So before he spent 7 dollars, he had those 7 dollars.

Add 7 with 95

95 + 7 = 102

PLS HELP ASAP ILL GIVE BRAINLKEST

Answers

Answer:

4th option

Step-by-step explanation:

Ten less than the product of a number and 45.​

Answers

Answer:

45*x-10

Step-by-step explanation:

10 less than a number would give you

x - 10

and the product of a number means your multiplying and your multiplying 45 so you would get

45*x

add them together and you get

45*x-10


Help please ASAP !

Answers

Tha last one PR=XY is not true.

It should be PR=XZ.

y=1/2x-4 in Standard Form

Answers

[tex]y =\dfrac 12 \cdot x -4\\\\\implies y = \dfrac{x-8}2\\\\\implies 2y = x-8\\\\\implies x -2y=8[/tex]

Emma but two identical bottles of shampoo. She uses 3/8 of one of them at home, and uses 7/10 of all of the remaining while she’s on Hollidays. In total, how much shampoo remains?

Answers

Answer:

37/40

Step-by-step explanation:

                                      3/8                              7/10

      80/40                   -       15/40              -          28/40                   =  37/40

two whole shampoo  -      uses at home    -      uses on holiday     =  left

Determine the domain of each graph:

Answers

Answer:

The 1st

Domain is (1,-3)

The second

Domain is (R)

The 3rd

Domain = (R)

The 4th

Domain =(-1,+infinity )

Respectively

Check the number or numbers that are in the solution set of the equation

below.

7x > 42

A. 14

B. 5

C.35

D. 6

E. 12

F9



Answers

Answer:

A, C, E, F

Step-by-step explanation:

when you multiply the numbers with 7 the answer is greater than 42

can someone help me plsss

Answers

Answer:

c=23/24

Step-by-step explanation:

 c+3/8=1/1/3

 c+3/8=4/3

c+9/24=32/24

        c=32/24-9/24

         =23/24

i need help fast please

Solve this and show steps

4.5×8-(0.4+9.6-(3.6-1.8))

Answers

Answer:

27.8

Step-by-step explanation:

You need to do brackets first

3.6-1.8 = 1.8

Then substitute

4.5 x 8- (0.4 + 9.6- 1.8)

0.4+9.6-1.8=8.2

4.5 x 8 - 8.2 =27.8

What is the measure of angle xyz

Answers

Answer:

Step-by-step explanation:

LET:

∠XYW=Y

X,Y and W are the angles of triangle so:

X + Y + W=180

3x+11+Y+5x+1=180

Y=180-12-8x

Y=168-8x

Now ∠XYW and ∠XYZ are the angles of a straight line:

∠XYW+∠XYZ=180

168-8x+12x-20=180

4x+148=180

4x=180-148

4x=32

x=32/4

x=8

Now substitute value of x in Y:

∠(12x-20)=12(8)-20

∠Y=76

Draw triangle GMT

PLS CREATE DRAWING!! refer to attachment

Answers

The angle between sides GM and MT is ∠M.

The 2 sides that include ∠T are MT and GT.

The angle between sides GT and MG is ∠G.

There's not much to say about this, but I can answer questions if you have any.

Answer Please will give brainliest.

Answers

Step-by-step explanation:

blue is natural: 1, 4, 0, 2 and root of 25.

green is whole: -9 and -15.

yellow is rational: 2/3

orange is irrational: pi and root of 15.

white is real numbers.

don't know about that purple one.

A glue company needs to make some glue that it can sell for $120 per barrel. It wants to use 150 barrels of glue worth $100 per barrel, along with some glue worth $150 per barrel and glue worth $190 per barrel. It must use the same number of barrels of $150 and S190 glue. How much of the $150 and $190 glue will be needed? How many barrels of $120 glue will be produced

Answers

4860 i think that is the answer

solve the equation.

[tex]\sqrt{x(x+2)} = 0[/tex]

Answers

[tex]\sqrt{x(x+2)} = 0 <=> x(x+2)=0\\<=> x=0 /or/ x+2=0 <=> x=0 /or/ x=-2[/tex]

ok done. Thank to me :>

Polly buys 6.8 yards of fabric for $28.90. What is the cost per yard?

Please help? :)​

Answers

Answer:

Polly has to pay $0.24 per yard of fabric.

Step-by-step explanation:

You simply have to divide the 6.8 yards by the $28.90 cost. The result is $0.235294118 dollars per yard, but since you can't have only half a cent, we will round it to the nearest hundredths and get $0.24 dollars.

Please help me solve this... I will mark you brainliest if it’s correct

Answers

(5 + 7x + 6)/2 = 3x + 9

7x + 11 = 6x + 18

7x - 6x = 7

x = 7

EF = 3x + 9

= 3(7) + 9

= 21 + 9

= 30
Other Questions
Two parallel chords PQ and MN are 3 cm apart on the same side of a circle where PQ = 7 cmand MN = 14 cm. Calculate the radius of the circle. What is .7899 rounded 4 decimal places 98546 dividido para46 Which expression represents 81 decreased by an unknown number?81a 81a81a 81 + a what inventions were particularly important in the development of industrialism STATION 5 ! GIVING BRAINLIEST TO WHOEVER ANSWER W AN GREAT EXPLNATION Hereditary spherocytosis (HS) is a disorder of red blood cells that causes the cells to be smaller and spherical instead of having the usual flattened, biconcave shape. The average diameter of normal red blood cells is 7.2m, and the average diameter of red blood cells in a person with HS was found to be 6.7m. The normal red blood cell has an average surface area of 136m2 and an average volume of 91m3.Which of the following provides an accurate calculation of the surface area to volume ratio of an HS red blood cell, as well as a prediction of its effect on the efficient transferring of oxygen compared to a normal red blood cell? what is the difference between ramayana and the painting about medium change the story Need a expert please a 25 -ft ladder rests against the side of a house. the distance between the top of the lader and the ground is 17 ft more than the distance between the base od the ladder and the bottom of the house. find both distances. what are the major source of foreign country? Chapter 3: Before the Time Traveller makes his appearance, the narrator explains that Which place value first determines which of the numbers 6.399 or 6.400 is the larger number?thousandthshundredthstenthsones *PLEASE HELP 50 POINTS +BRAINLIEST*What was one reason the Holy Roman emperors failed to build a unified nation-state in Germany?They were distracted by the Crusades.They were distracted by the Crusades.They were unable to control their vassals.They were unable to control their vassals.They were excommunicated by the Pope.They were excommunicated by the Pope.They lacked financial resources. XYZ Company had 200,000 shares of common stock outstanding on December 31, 2020. On July 1, 2021, XYZ issued an additional 44,000 shares for cash. On January 1, 2021, XYZ issued 16,000 shares of convertible preferred stock. The preferred stock had a par value of $100 per share and paid a 6% dividend. Each share of preferred stock is convertible into 8 shares of common. During 2021, XYZ paid the regular annual dividend on the preferred and common stock. Net income for the year was $270,000. Required: Calculate XYZ's basic and diluted earnings per share for 2021. (Round your answers to 2 decimal places.) Can someone review this and give feedback it is about The Other Wes Moore book.Many people are given another chance after doing wrong so then they can fix their mistakes and grow as a person. Some people decide to take the second chance they're given and others take it as a get out of jail free card. In Wes Moore's book "The Other Wes Moore" He talks about how he and another kid named Wes Moore both did some not-so-amazing things as kids. He also talks about the choices that led up to it and what happened after they were given second chances. Both Wes Moore's were given second chances after they made a mistake, one took it and went on a better path and the other ignored it and ended up in prison.Moore was eight when he first ended up in handcuffs, he called his brother and was given his first of many second chances the book states Three hours later, Wes was released under the care of Tonys Father, and he was back at his house before his mother got home from her job. It was years before Wess mom found out her son had been arrested that day (Moore 35). That was Moores first major mistake in a road that only went downhill. He later decided to not attend school and to skip it and hang out with his friends, one day he drank alcohol and paid the price for it his mom even said Well, at least now you know how bad it feels and you will stay away from drinking when he got a hangover (Moore 62). What is the equation for the line in slope-intercept form? Triangle IJK has the coordinates listed:Where is J' after a reflection over the y-axis? I will give a 5-star answer and BrainlestDirect contact is necessary for which type of energy transfer?A. ConductionB. Sound WavesC. ConvectionD. Radiation please help me I really need help ben put 1000 into a savings account. the interest rate was compound at 0.65% per year. at the end of x years he had made 53.20 in interest show that x=8