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kaheart [24]
2 years ago
6

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?
Mathematics
1 answer:
Akimi4 [234]2 years ago
8 0

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

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Not sure what your asking here
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2 years ago
Does anyone know the answers to these?
dem82 [27]

Step-by-step explanation:

a. The point estimate is the mean, 47 days.

b. The margin of error is the critical value times the standard error.

At 31 degrees of freedom and 98% confidence, t = 2.453.

The margin of error is therefore:

MoE = 2.453 × 10.2 / √32

MoE = 4.42

c.  The confidence interval is:

CI = 47 ± 4.42

CI = (42.58, 51.42)

d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.

e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.

3 0
3 years ago
Kent and Bradley both work at a car dealership. Kent makes $10/hour + 3% on the amount of sales he completes. Bradley only makes
Masteriza [31]

Answer: There is difference of $660 in their paychecks.

Step-by-step explanation:

Since we have given that

Number of hours in one week they worked = 40

Amount of sales = $78000

Kent makes $10 per hour plus 3% on the amount of sales .

So, the equation for Kent becomes,

10\times 40+\frac{3}{100}\times 78000\\\\=400+3\times 780\\\\=400+2340\\\\=\$2740

Similarly, Bradley only makes $7 per hour but he makes 4% on the amount of his sales .

So, the equation for Bradley becomes,

7\times 40+\frac{4}{100}\times 78000\\\\=280+4\times 780\\\\=280+3120\\\\=\$3400

hence, the difference between of their paychecks is given by

\$3400-\$2740\\\\=\$660

Therefore, there is difference of $660 in their paychecks.

3 0
2 years ago
780 is what percent of 540?
zaharov [31]

Answer:

144.44%

Step-by-step explanation:

780/540 = 1.44444 * 100 (for each percent) = 144.44 %

4 0
2 years ago
Read 2 more answers
You ask a friend to think of a number from 7 to 14. What is the probability that his number will be an even number? Answer as a
8_murik_8 [283]

Answer:

1/2

Step-by-step explanation:

Not sure but

I am assuming we have 8 integers :

All or (A) = {7,8,9,10,11,12,13,14} = n(A) = 8

Hence, the probability of any one outcome is 1/8.

Therefore, as you can detect, there are 4 numbers that are even numbers which means :

Even or (E) = {8, 10, 12, 14} = n(E) = 4

So, let E imply this occurrence

E x A

= 4 x 1/8

= 4/8

= 1/2

3 0
3 years ago
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