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

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Joined: 10 Oct 2003
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If the letters of the word CHASM are rearranged to form 5 [#permalink]  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
GMAT Instructor
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Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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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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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

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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
GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
Followers: 13

Kudos [?]: 52 [0], given: 0

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.
_________________

Best,

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

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