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Chairs in a row

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by GmatKiss » Fri Oct 28, 2011 1:12 pm
There are five empty chairs in a row. If six men and four women are waiting to be seated, what is the probability that the seats will be occupied by two men and three women?
A) 4/21
B) 5/21
C) 8/21
D) 9/21
E) 11/21
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by shankar.ashwin » Fri Oct 28, 2011 7:08 pm
(6C2 * 4C3)/10C5 = 5/21
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by Anurag@Gurome » Fri Oct 28, 2011 9:51 pm
GmatKiss wrote:There are five empty chairs in a row. If six men and four women are waiting to be seated, what is the probability that the seats will be occupied by two men and three women?
A) 4/21
B) 5/21
C) 8/21
D) 9/21
E) 11/21
Total number of ways of choosing 5 people out of 10 people = 10C5 = 10!/(5! * 5!) = (10 * 9 * 8 * 7 * 6)/(5 * 4 * 3 * 2 * 1) = 2 * 9 * 2 * 7 = 252
Number of ways to choose 2 men out of 6 men = 6C2 = 6!/(4! * 2!) = (6 * 5)/2 = 15
Number of ways to choose 3 women out of 4 women = 4C3 = 4!/(3! * 1!) = 4
Therefore, the probability that the seats will be occupied by 2 men and 3 women = (15 * 4)/252 = 5/21

The correct answer is B.
Anurag Mairal, Ph.D., MBA
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