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If the letters of the word CHASM are rearranged to form 5

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If the letters of the word CHASM are rearranged to form 5 [#permalink] New post 04 Nov 2003, 04:03
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
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 [#permalink] New post 04 Nov 2003, 07:59
Consider a coding system where C, H, A, S, M = 2, 3, 1, 5, 4 respectively. We want to know the rank of code 23154.

Let's count all of the possible combinations below 23154.

We know that any code starting with 1 is less so we have 4! = 24 possibilities.

We also know that any cod starting with 21 is less so we have 3! or 6 additional possibilities.

For codes starting with 23XXX, only 23145 is less than 23154. so we have a total of 31 codes less than 23154 so the rank of cod 23154 is 32 and the answer, IMO, is (3).
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 [#permalink] New post 05 Nov 2003, 00:35
My approach:

ACHMS is the first word. CHMS are arranged in 4!=24 ways, so
CAHMS is the twenty-fifth word. HMS are arranged in 3!=6 ways, so
CHAMS is the thirty-first word
CHASM is the thirty-second
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 [#permalink] New post 05 Nov 2003, 02:55
stolyar wrote:
My approach:

ACHMS is the first word. CHMS are arranged in 4!=24 ways, so
CAHMS is the twenty-fifth word. HMS are arranged in 3!=6 ways, so
CHAMS is the thirty-first word
CHASM is the thirty-second


That is essentially exactly same method as mine.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

  [#permalink] 05 Nov 2003, 02:55
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If the letters of the word CHASM are rearranged to form 5

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