Permutation & Combination Answers

Permutation and Combination - Quant/Math - CAT 2007

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Question 4 the day: September 08, 2003

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

Question:

If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

(1) 24
(2) 31
(3) 32
(4) 30

Correct Answer - (3)

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Solution:


The 5 letter word can be rearranged in 5! Ways = 120 without any of the letters repeating.

The first 24 of these words will start with A.

Then the 25th word will start will CA _ _ _. The remaining 3 letters can be rearranged in 3! Ways = 6. i.e. 6 words exist that start with CA.

The next word starts with CH and then A, i.e., CHA _ _. The first of the words will be CHAMS. The next word will be CHASM.

Therefore, the rank of CHASM will be 24 + 6 + 2 = 32.