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

The number of words of 4 consonants and 3 vowels can be made from 15 c

1.	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» 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!.

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