Password Combination

Question

Here is the answer I want to ask... Please help to solve this question.

The password of a system consists 3 capital letters selected from A-Z.

Repetition use of any letters is allowed.

Find the maximum number of different passwords that can be formed if ...

(a) there is no restriction.

i think a is = 26^3=17576

(b) the password contains at least one vowel.

(c) the password begins with A or ends with Z.

Answer 1

a) yes

b) this would be all passwords minus those containing no vowels (or all consonants) =

26^3 - 21^3

c) n(A U B) = n(A) + n(B) - n(AB)

A = number starting with an A

B = number ending with a Z

AB = number beginning with an A and ending with a Z

A can have any second and third letter

B can have any first and second letter

AB can have any second letter

n(A) + n(B) - n(AB) =

26^2 + 26^2 - 26 =

26(26 + 26 - 1) = 26 * 51