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In how many different ways can the letters in the word

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In how many different ways can the letters in the word [#permalink] New post 19 Jan 2006, 10:54
00:00
A
B
C
D
E

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(N/A)

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In how many different ways can the letters in the word "LEVEL" be arranged.
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 [#permalink] New post 19 Jan 2006, 11:35
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, 11:41, edited 1 time in total.
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 [#permalink] New post 19 Jan 2006, 11:39
LEVEL - itself represents 2! * 2! combinations.

So total possible combinations = 5!/(2!*2!) = 30
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 [#permalink] New post 19 Jan 2006, 16:32
Total words = 5

Repeat word E (twice) and L (twice)

So = 5!/(2!*2!) = 30
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 [#permalink] New post 19 Jan 2006, 17:35
L - 2
E - 2
V - 1

Total number of ways = 5!/2!2! = 30
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 [#permalink] New post 19 Jan 2006, 20:02
Example: To find all permutations on A B C C
Answer: ABCC, ACBC, ACCB,
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
  [#permalink] 19 Jan 2006, 20:02
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