Permutation & Combination Answers

Permutation and Combination - Quant/Math - CAT 2007

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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

Correct Answer - (2)

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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!