Permutation & Combination Answers

Permutation and Combination - Quant/Math - CAT 2007

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Question 4 the day: June 19, 2003

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

Question:

In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?

(1) 9!/4
(2) 9!/(4!*5!)
(3) 4!*5!
(4) None of these

Correct Answer - (3)

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Solution:


The word EDUCATION is a 9 letter word, with none of the letters repeating.

The vowels occupy 3, 5, 7^th and 8^th position in the word and the remaining 5 positions are occupied by consonants

As the relative position of the vowels and consonants in any arrangement should remain the same as in the word EDUCATION, the vowels can occupy only the aforementioned 4 places and the consonants can occupy 1^st, 2^nd, 4^th, 6^th and 9^th positions.

The 4 vowels can be arranged in the 3^rd, 5^th, 7^th and 8^th position in 4! Ways.

Similarly, the 5 consonants can be arranged in 1^st, 2^nd, 4^th, 6^th and 9^th position in 5! Ways.

Hence, the total number of ways = 4! * 5!.