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) ^{16}C_{7} * 7!
(2) ^{12}C_{4} * ^{4}C_{3} * 7!
(3) ^{12}C_{3} * ^{4}C_{4}
(4) ^{12}C_{4} * ^{4}C_{3}
Correct Answer  (2)
Solution:
4 consonants out of 12 can be selected in ^{12}C_{4} ways.
3 vowels can be selected in ^{4}C_{3} ways.
Therefore, total number of groups each containing 4 consonants and 3 vowels = ^{12}C_{4} * ^{4}C_{3}
Each group contains 7 letters, which can be arranging in 7! ways.
Therefore required number of words = ^{12}4 * ^{4}C_{3} * 7!
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