Permutation and Combination - Quant/Math - CAT 2007
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)
Solution:
The word EDUCATION is a 9 letter word, with none of the letters repeating.
The vowels occupy 3, 5, 7th and 8th 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 1st, 2nd, 4th, 6th and 9th positions.
The 4 vowels can be arranged in the 3rd, 5th, 7th and 8th position in 4! Ways.
Similarly, the 5 consonants can be arranged in 1st, 2nd, 4th, 6th and 9th position in 5! Ways.
Hence, the total number of ways = 4! * 5!.
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