Question

The number of words of 4 consonants and 3 vowels can be made from 15 consonants and 5 vowels, if all the letters are different is ________

(a) 3! * ^12C5

(b) ^16C4 * ^4C4

(c) 15! * 4

(d) ^15C4 * ^5C3 * 7!

The question was asked in an interview for internship.

I'd like to ask this question from Counting in division Counting of Discrete Mathematics

Answer 1

The correct answer is (d) ^15C4 * ^5C3 * 7!

The best explanation: There are 4 consonants out of 15 can be selected in ^15C4 ways and 3 vowels can be selected in ^5C3 ways. Therefore, the total number of groups each containing 4 consonants and 3 vowels = ^15C4 * ^4C3. Each group contains 7 letters which can be arranged in 7! ways. Hence, required number of words = ^15C4 * ^5C3 * 7!.