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Problem Solving: Combinations

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Intern
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Problem Solving: Combinations [#permalink] New post 07 Jul 2007, 09:44
Please provide answer with suitable explaination for the below problem. Thanks in advance :)
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From the word ZEBRA, how many different letter combinations can be arranged by using the foregoing letters?

A. 20 B. 60 C. 100 D. 120 E. 150
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 [#permalink] New post 07 Jul 2007, 10:08
This question is from the GMATClub Question Collection, and below is the explaination I came across-

Answer- E. If not repeating letters, which would sound quite reasonable, then it is all possible combinations with 5, 4, 3, 2, and 1 letters. 5!+ P(5,4)+P(5,3)+P(5,2)+5 120 + 5 + 10 + 10 + 5 = 150

Can you let me know your thoughts on this. Thanks!
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 [#permalink] New post 07 Jul 2007, 10:30
vsaxena wrote:
This question is from the GMATClub Question Collection, and below is the explaination I came across-

Answer- E. If not repeating letters, which would sound quite reasonable, then it is all possible combinations with 5, 4, 3, 2, and 1 letters. 5!+ P(5,4)+P(5,3)+P(5,2)+5 = 120 + 5 + 10 + 10 + 5 = 150

Can you let me know your thoughts on this. Thanks!


Total possible arrangements =
no. of [5 letter comb. + 4 letter comb. + 3 letter comb. + 2 letter comb. + 1 letter comb.] = 5! + 5P4 + 5P3 + 5P2 + 5P1 = 150

'P' stands for permutation.

Hope this helps. :-D
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 [#permalink] New post 07 Jul 2007, 10:37
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 [#permalink] New post 07 Jul 2007, 11:16
Thanks for your answers.

But I still don't understand the logic provided in the explaination & meaning of "foregoing"!! If I consider author's explaination (5!+ P(5,4)+P(5,3)+P(5,2)+5 = 120 + 5 + 10 + 10 + 5 = 150), then I should be getting following answer:

5! = 120
P(5,4) = 120
P(5,3) = 60
P(5,2) = 20
5
--------------
325
--------------

& not
120 + 5 + 10 + 10 + 5 = 150!!
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 [#permalink] New post 07 Jul 2007, 11:20
I think the question should be rephrased as under:

How many different 1-letter, 2-letter, 3-letter, 4-letter and 5-letter arrangements are possible from the word ZEBRA?

Make sense???
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 [#permalink] New post 07 Jul 2007, 11:23
And yes, I am advocating for 325 :) Answer choice 150 still doesnt make sense to me. Thanks everybody for your posts anyways :)
  [#permalink] 07 Jul 2007, 11:23
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