Alfred wants to become a member of an online discussion forum. The website requires him to create a password. The password must consist of 5 characters, of which 3 must be letters and 2 must be digits. The first character of the password must be a letter. Also, repetition of the same letter in the password is not permitted but repetition of digits is permitted. How many possible ways can Alfred create the password?
So I know the answer is 9,360,000 but I got 18,720,000. This is because I thought the partition is 4! / (2! * 1! * 1!) but apparently the partition is 4! / (2! * 2!) and this confuses me. I thought that since the letters can't be repeated, we'd put one unique letter in one group, the other unique letter in the other group, and the two repeated digits in the last group. Can somebody explain this to me?

Answers

Answer 1

Answer:

Alfred can create the password in 9,360,000 possible ways

Step-by-step explanation:

Given the data in the questions;

Password of five characters must contain; three letters and 2 digits

[][][][][]

Now, using the five boxes above which as to be filled with three letters and two digits, such that; The first character of the password must be a letter and  repetition of the same letter in the password is not allowed while repetition of digits is allowed.

Now,

we know that there are 26 alphabets in English language, so the first box can be filled in 26 ways { must be a letter }

next four will be filed with two letters and two digits

so two boxes from the four can be chosen in the following ways;

⇒ ⁴C₂ = 4! / ( 2!(4-2)! = 24 / 4 = 6  { ways }

now for each choice, we can fill the chosen two boxes with letters in;

⇒ 25 × 24 = 600 { ways}

and the next two by digits; ( 0, 1, 2, ..... 9)

⇒ 10 × 10 = 100 { ways }

So in total, the possible number of ways he can create a password is;

⇒ 26 × 6 × 600 × 100

= 9,360,000 possible ways

Therefore, Alfred can create the password in 9,360,000 possible ways


Related Questions

Write the slope intercept form of the equation of the line. x + 8y = 24​

Answers

The answer is y= -1/8x+3

Jamie, Daniel, and Taylor want apples. Jamie cuts 5 apples into equal-sized pieces. If they all eat the same amount, how many apples will each person eat​

Answers

Answer:

1⅔

Step-by-step explanation:

Asking I'd say it's simply 5 apples divided by

the three of them to get 1⅔

If you can drive 340 miles in 5 hours, what is the unit rate? *
(2 Points)
Enter your answer

Answers

I believe it would be 68 miles per hour! To find the unit rate here you would divide miles by hours, or 340 by 5, which would give you 68.

The Total cost to rent 5 chairs and 3 tables is $31 dollars. What is the cost to rent each chair and each table? No links please

Answers

Answer:

b

Step-by-step explanation:

The expression (g^2)^4 is equivalent to g^m. What is the value of m?

^ means exponents

Answers

Answer:

m = 8

Step-by-step explanation:

4 x 2

you just have to multiply exponents

My car magazine reports the numbers of miles driven for different amounts of fas for
Three car. Which car travels the fastest on 1 gallon of gas explain

Answers

Answer:

yes and no a.a

Step-by-step explanation:

Car A travels the fastest on 1 gallon of gas.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. The unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that car, the magazine reports the numbers of miles driven for different amounts of fas for Three car.

Consider us solving for the miles per gallon of individual cars

A. miles driven =140

A gallons= 5

x= 140/5

x= 28 miles per gallon

To learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

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“What is the gradient of the graph shown?”
someone please help I don’t understand how to do this.

Answers

Answer:

Step-by-step explanation:

It is easy to see that (-2, 0) and (0, -4) are points on the line.

gradient = (difference of y-coordinates)/(difference of x-coordinates) = (0-(-4))/(-2-0) = 4/(-2) =  -2

Two more than five times a number is less than or equal to 47
WRITE THAT AS AN INEQUALITY. IF YOU DON'T KNOW WHAT THAT IS THIS IS AN EXAMPLE 3g - 4 ≥ 17

Answers

Answer:


2+5x>47 or 2+5x=47

factorise x^{2} +2x-24[/tex]

Answers

Answer:

(x + 6)(x - 4)

Step-by-step explanation:

x² + 2x - 24

(x + 6)(x - 4)

-4 and +6 multiply to 24 and add to +2.

Help shefeejhrhrhhtuy

Answers

Answer:

c. 80,360

Step-by-step explanation: multiply the number of cases they make each day by the amount of pastries each case contains

The large rectangle below represents one whole.

What percent is represented by the shaded area????

Answers

40% is shaded :))))))

Answer:

40%

Step-by-step explanation:

Because there are 5 rectangle total, we can dive 100% into 5 parts.

Each part is then 20%, there are 2 shaded rectangles thus the answer is 40%.

If the radius is 25 mm, what is the Diameter

Answers

Answer:

7.96

Step-by-step explanation:

Jodie has $70 to spend on flowers for a school event. She wants to buy roses for $24 and spend the rest on lilies. Each lily flower costs $12. How many can she purchase without going over her budget?

Answers

Answer:

only 3

Step-by-step explanation:

she can purchase three or 3 without going over budget

PLZZZZ HELPPP MEE!!!!!

Answers

Answer:

-60

Explanation:

6x(2x-5) always do what's in the parentheses first

6x(-10)

= -60

Which number line shows a graph of the inequality x > -25?

Answers

Answer:

Step-by-step explanation:

   o--------------------------->

[tex]<------------>\\ -25 -24 -23 -22 -21 -20[/tex]

> means an open circle on -25, and a line pointing to the right because it's greater than.

Options C and D number lines show a graph of the inequality x > -25 that lies on the positive side.

What is inequality?

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

We have given a condition we need to find which number line shows a graph of the inequality x > -25.

We can see in the graph that the number line of options 1 and 2 doesn't show the inequality x > -25 because the point lies on the negative side of the number line.

But the number line in the options C and D shows the inequality x > -25.

Learn more about inequality ;

https://brainly.com/question/20383699

sjdjwkfmwkfkekfmkdekjejwje

Answers

Answer:

I think yes but it could be no. Sorry if I am wrong but it should be yes.

Find the measure of 41.
{
839
41
4 1 = [?]
Enter

Answers

<1=97°

Answer:

<1+83=180 co interior angle

<1=180-83=97°

Answer:

solution given:

<1+<83°=180°[co- interior angle]

<1=180°-<83°=97°

<1=97° is your answer

What percent of 84 is 42

Answers

Sorry if I’m wrong but i believe it’s 50.

A brochure claims that the average maximum height a certain type of plant is 0.7 m. A gardener suspects that this estimate is not accurate locally due to soil conditions. A random sample of 43 plants is taken. The mean height of the plants in the sample is 0.65m. Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is different from 0.7m. Assume that the population standard deviation is 0.2 m.

Answers

Answer:

We accept the null hypothesis, that is, that the population mean is not different from 0.7.

Step-by-step explanation:

A brochure claims that the average maximum height a certain type of plant is 0.7 m.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 0.7[/tex]

A gardener suspects that this estimate is not accurate locally due to soil conditions.

Hypothesis test to determine whether the population mean is different from 0.7m, which means that the alternate hypothesis is:

[tex]H_{a}: \mu \neq 0.7[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that [tex]\mu = 0.7[/tex]

A random sample of 43 plants is taken. The mean height of the plants in the sample is 0.65m.

This means, respectively, that [tex]n = 43, X = 0.65[/tex]

Assume that the population standard deviation is 0.2 m.

This means that [tex]\sigma = 0.2[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.65 - 0.7}{\frac{0.2}{\sqrt{43}}}[/tex]

[tex]z = -1.64[/tex]

Pvalue of the test:

Since we are testing that the mean is different of a value, and z is negative, the pvalue of the test is 2 multiplied by the pvalue of z = -1.64

z = -1.64 has a pvalue of 0.0505

2*0.0505 = 0.101

Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is different from 0.7m.

0.101 > 0.01, which means that we accept the null hypothesis, that is, that the population mean is not different from 0.7.

what is the slope of the line.

Answers

Answer:

m=3/2 or m=1.5

Step-by-step explanation:

slope formula:

m=(y1-y2)/(x1-x2)

in order to get this we need two points such as (3,0) and (1,-3) which are points on this line. So:

m=(0-(-3))/(3-1)

m=3/2 or m=1.5

First one to answer this gets BRAINLIEST no cap. (Look at the pic)

Answers

Answer:

36.

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

The formula to solve this is a+b)/2*h

4+5=9

9/2=4.5

4.5*8= 36

How many cannonballs are there in the eighth figure

Answers

Answer:

36

Step-by-step explanation:

Please help me and happy april fools day! B)

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Answer:

A,C,D,F

Step-by-step explanation:

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Answer:

A

Step-by-step explanation:

When finding out which number is the greatest, I would convert these numbers to numerals with decimals for easier comparison.

3[tex]\sqrt{5}[/tex] is approximately 6.71.

6[tex]\frac{1}{4}[/tex] is 6.25

6.55 is, well 6.55.

From here, we can tell that 6.71 is the greatest, followed by 6.55 and 6.25 is the smallest. Thus, the order in descending order should be 3[tex]\sqrt{5}[/tex], 6.55 then 6[tex]\frac{1}{4}[/tex], which is Option A.

Graph the inequality n > 1.8

Answers

Answer:

Open circle going right. <-- graphed

Step-by-step explanation:

1billion is the correct answerStep-by-step explanation:

Find the perimeter of the figure. due today

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Answer:

24 in

Step-by-step explanation:

5in + 4in + 9in + 5in + (4in - 3in) = 24in

Ryan's Study Schedule
Subject Subject (Hours)
2
Math
2
3
1
Science
1-
2
1
English
3
1
Social Studies
1
4
What is the closest amount to the hours Ryan spends studying?
7 hours
8 hours
0 5 hours
O 9 hours

Answers

math and english give you a total of 4 hours. and social studies and science gives you a total of 2 3/4 hours. add them up, and the closest he will spend to studying is 7 hours

Let f be defined by the function f(x) = 1/(x^2+9)
(a) Evaluate the improper integral [tex]\int\limits^{∞}_3 {f(x)} \, dx[/tex] or show that the integral diverges
(b) Determine whether the series ∑n=3∞ f(n) converges or diverges State the conditions of the test used for determining convergence or divergence
(c) Determine whether the series ∑n=1∞(−1)n(en⋅f(n))=∑n=1∞(−1)n(n2+9)en converges absolutely, converges conditionally, or diverges (image put below)

Answers

(a)

[tex]\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}[/tex]

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

[tex]\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt[/tex]

[tex]=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}[/tex]

(b) The series

[tex]\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}[/tex]

converges by comparison to the convergent p-series,

[tex]\displaystyle\sum_{n=3}^\infty\frac1{n^2}[/tex]

(c) The series

[tex]\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}[/tex]

converges absolutely, since

[tex]\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}[/tex]

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

5th grade math. correct answer will be marked brainliest

Answers

Answer:

8 1/12 boxes

Step-by-step explanation:

Your first step to solve this problem is to convert those fractions to a common denominator. I would choose 12. So your first would be 4 4/12 and your second would be 3 9/12. You would then add those up and get 8 1/12 boxes of muffins bought at the bake sale.

At a Beirut market, oranges are priced at $1.29/KG. Ms. X buys 10 oranges that have a total weight of 4.82 kgs. What is the average price per orange that she pays?

Answers

Answer:

The average price of each orange is $0.62.

Step-by-step explanation:

Given that at a Beirut market, oranges are priced at $ 1.29 per kilo, and Ms. X buys 10 oranges that have a total weight of 4.82 kilograms, to determine what is the average price per orange that she pays must perform the following calculation:

(4.82 x 1.29) / 10 = X

6.21 / 10 = X

0.62 = X

Thus, the average price of each orange is $ 0.62.

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