Sets and Counting Consider the following set U M A T H I S F

Sets and Counting

Consider the following set: U= {M, A, T, H, I, S, F, U, N}

How many five-letter words (including nonsense words) are possible if letters can repeat, but the second letter must be a vowel and the last letter must be a \"T\"?

(Please show how you solved this problem)

Solution

There are 9 letters here.

For the first, 3rd, and 4th letters, there are 9 choices.

For the second letter, there are only 3 (A, I, U).

For the last letter, there is only 1 (T).

Thus, there are 9*3*9*9*1 = 2187 ways [ANSWER]