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# You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs

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Joined: 27 Jul 2011
Posts: 147
You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs  [#permalink]

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Updated on: 22 Jun 2012, 00:16
1
00:00

Difficulty:

75% (hard)

Question Stats:

47% (00:31) correct 53% (00:53) wrong based on 77 sessions

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You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?

A. 5
B. 6
C. 9
D. 12
E. 18

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If u can't jump the 700 wall , drill a big hole and cross it .. I can and I WILL DO IT ...need some encouragement and inspirations from U ALL

Originally posted by BukrsGmat on 21 Jun 2012, 23:15.
Last edited by Bunuel on 22 Jun 2012, 00:16, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs  [#permalink]

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22 Jun 2012, 00:16
4
2
You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?

A. 5
B. 6
C. 9
D. 12
E. 18

Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:
XYZ
YZX
ZXY

And:
XYZ
ZXY
YZX

Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible is 2*6=12.

Hope it's clear.

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Posts: 9163
Re: You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs  [#permalink]

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09 Aug 2018, 10:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs &nbs [#permalink] 09 Aug 2018, 10:29
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