Question

A website randomly creates an initial password for people when they first sign up for an account. The password consists of five letters, and cannot include numbers or special characters. The letters of the password cannot repeat. What is the approximate probability that a password will have no vowels? What is the approximate probability that the first letter of the password will be m?

Answer 1

The answers are C: 0.30934 for the first one, and B: 0.03846 for the second. 

Answer 2

This is a non replacement question, so each letter decreases by 1.

No vowels
The question actually starts right here. The preamble tells us that we can only use letters, no numbers, and no symbols. We are not asked to do anything. The first question makes no mention of there being anything special about m. It can be there or it most likely is not. This part of the problem is the first part.

First Part
I'm not going to deal with y. I will declare it to be a consonant.
There are 5 vowels. None of them can be chosen.
21 letters remain (including the m since it has not been limited in any way yet).

21 * 20 * 19 * 18 * 17
================
26 * 25 * 24 * 23 * 22

2441880 / 7893600
0.30934
Note: If your calculator has nPr on it, you can enter 21 nPr 5 to eliminate all the typing.

Second Part
No vowels and the first letter MUST be m
1 * 20 * 19 * 18 * 17/( 26 * 25 * 24 * 23 * 22)
116200/7893600 = 0.01473

Vowels and the first letter m.
1 * 25 * 24 * 23 * 22/ 7893600 = 0.03846