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# In how many different ways can the letters in the word

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Senior Manager
Joined: 03 Nov 2005
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Location: Chicago, IL
In how many different ways can the letters in the word [#permalink]

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19 Jan 2006, 11:54
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In how many different ways can the letters in the word "LEVEL" be arranged.
_________________

Hard work is the main determinant of success

Kudos [?]: 67 [0], given: 17

Director
Joined: 17 Dec 2005
Posts: 544

Kudos [?]: 40 [0], given: 0

Location: Germany

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19 Jan 2006, 12:35
edited

You've five letters; they can lead to 5! permutaions of whom some are double, namely those in which the placements E's and L's are counted twice. To get them out divide

5!/ 2!*2! = 30

The two 2's represent the ways the two letter can be arranged on theit respective places.

Last edited by allabout on 19 Jan 2006, 12:41, edited 1 time in total.

Kudos [?]: 40 [0], given: 0

SVP
Joined: 14 Dec 2004
Posts: 1685

Kudos [?]: 168 [0], given: 0

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19 Jan 2006, 12:39
LEVEL - itself represents 2! * 2! combinations.

So total possible combinations = 5!/(2!*2!) = 30

Kudos [?]: 168 [0], given: 0

CEO
Joined: 20 Nov 2005
Posts: 2893

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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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19 Jan 2006, 17:32
Total words = 5

Repeat word E (twice) and L (twice)

So = 5!/(2!*2!) = 30
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Kudos [?]: 322 [0], given: 0

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5036

Kudos [?]: 436 [0], given: 0

Location: Singapore

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19 Jan 2006, 18:35
L - 2
E - 2
V - 1

Total number of ways = 5!/2!2! = 30

Kudos [?]: 436 [0], given: 0

Senior Manager
Joined: 13 Jun 2005
Posts: 252

Kudos [?]: 19 [0], given: 0

Location: Haverhill, MA

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19 Jan 2006, 21:02
Example: To find all permutations on A B C C
BACC, BCAC, BCCA,
CABC, CBAC, CBCA,
CACB, CCAB, CCBA
There are 12 orders, or 12 permutations in total.

P( permutation of n objects with n1 identical ones)

= n!/ n1!

Example of ABCC:
n = 4; (A,B,C,C)
n1= 2; (C,C)
n!/ n1! = 4! / 2! = (4 x 3 x 2 x 1)/ (2 x 1) = 12

Kudos [?]: 19 [0], given: 0

19 Jan 2006, 21:02
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