Question

A randomly generated password has four characters. Each character is either A, B, C, D, E or F or a number from 0 - 9. Each character in the password can only be used once. What is the probability that a password has only one number?

A:10/91
B:9/91
C:5/182

Answer 1

5/182

Explanation:

Answer 2

Correct option: A -> 10/91

Explanation:

If the password has only one number, it has three characters.

So first we can do a combination of 4 choose 3, as the characters and numbers can be at any position, then we multiply by the probability of each space having a character or number:

Combination of 4 choose 3: 4!/3! = 4

First character: 6 possibilities over a total of 16: 6/16 = 3/8

Second character: 5 possibilities over a total of 15: 5/15 = 1/3

Third character: 4 possibilities over a total of 14: 4/14 = 2/7

First number: 10 possibilities over a total of 13: 10/13

Probability: 4 * (3/8) * (1/3) * (2/7) * (10/13) = (2*5)/(7*13) = 10/91

Correct option: A