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### Permutation and Combination - Quant/Math - CAT 2016

Question 4 the day: October 08, 2003

The question for the day is from the topic Permutation and Combination.

Question:
How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?

(1) 16C7 * 7!
(2) 12C4 * 4C3 * 7!
(3) 12C3 * 4C4
(4) 12C4 * 4C3

Solution:

4 consonants out of 12 can be selected in 12C4 ways.

3 vowels can be selected in 4C3 ways.

Therefore, total number of groups each containing 4 consonants and 3 vowels = 12C4 * 4C3

Each group contains 7 letters, which can be arranging in 7! ways.

Therefore required number of words = 124 * 4C3 * 7!

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