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7 boys and 9 girls are in a club. In how many ways can they

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7 boys and 9 girls are in a club. In how many ways can they [#permalink]

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03 Jun 2004, 01:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

7 boys and 9 girls are in a club. In how many ways can they elect 4 different officers designated by A. B, C, D if

a. A and B must be boys and C and D must be girls?

b. two of the officers must be boys and two of the officers must be girls?

Answers are : a.) 3024, and for b)18144

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03 Jun 2004, 02:10
7 boys and 9 girls are in a club. In how many ways can they elect 4 different officers designated by A. B, C, D if

a. A and B must be boys and C and D must be girls?

2 boys from 7 can be selected in 7C2 ways and these can be arraanged among themselves in 7C2 X 2 Ways since the question is specific that A & B should be boys. Similarly, 2 girls from 9 can be selected and arranged in 9C2 X 2. So, the total number of ways they can be elected is 7C2 X 2 X 9C2 X 2 = 3024

b. two of the officers must be boys and two of the officers must be girls?
Since the question is not specific about the designations, as usual we select the boys and gorls in 7C2 X 9C2 and these 4 can be arranged in 4! ways. So, the total number of ways they can be elected is 7C2 X 9C2 X 4! = 18040 Ways.
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Mayur

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03 Jun 2004, 18:52
Thanks for the help Mayur. I understood the procedure. Clear explaination.

Regards
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03 Jun 2004, 18:52
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