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Bag of 9 letters

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by surajgarg » Tue Aug 10, 2010 7:16 am
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

OA later.
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by Rahul@gurome » Tue Aug 10, 2010 8:56 am
surajgarg wrote: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

OA later.
Let us consider the 1st row:
Then one letter can be placed in row 1 in 3! = 3*2*1 = 6 ways
2nd letter can be placed in row 2 in 2! = 2 ways
3rd letter can be placed in 3rd row in 1! = 1 way

Total no. of ways = 6*2 = 12 ways
The correct answer is [spoiler](D)[/spoiler].
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