Question

How many words with seven letters are there that start with a vowel and end with an A? Note that they don’t have to be real words and letters can be repeated.

(a) 45087902

(b) 64387659

(c) 12765800

(d) 59406880

This question was posed to me in an interview for job.

My query is from Fundamental Principle of Counting topic in division Counting of Discrete Mathematics

Answer 1

Right option is (d) 59406880

Explanation: The first letter must be a vowel, so there are 5 choices. The second letter can be any one of 26, the third letter can be any one of 26, the fourth letter can be any one of 26 and fifth and sixth letters can be any of 26 choices. The last letter must be an A, so there is only 1 choice. By the basic counting principle, the number of ‘words’ is 5 × 26 × 26 × 26 × 26 × 26 × 1 = 59406880.