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Probability Question

by sunny.bhasin » Sat Jun 11, 2011 3:05 am
Q) The "Cruz" club has just opened its membership. 12 women and 10 men have applied for the membership. In how many ways can 10 women and 8 men be selected if two particular women and 2 particular men need to be compulsorily selected?

1200

1820

1440

2970

1260

Can someone explain this?
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by Anurag@Gurome » Sat Jun 11, 2011 3:13 am
sunny.bhasin wrote:Q) The "Cruz" club has just opened its membership. 12 women and 10 men have applied for the membership. In how many ways can 10 women and 8 men be selected if two particular women and 2 particular men need to be compulsorily selected?
As 2 particular women and 2 particular men need to be compulsorily selected, we have to select (10 - 2) = 8 women out of (12 - 2) = 10 women and (8 - 2) = 6 men out of (10 - 2) = 8 men.

Total numbers of ways to select 6 men out of 8 = 8C6 = 28
Total numbers of ways to select 8 women out of 10 = 10C8 = 45

Hence, total number of ways of selection = 28*45 = 1260

The correct answer is E.
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by sunny.bhasin » Sat Jun 11, 2011 3:19 am
It clears my doubt.Thanks!
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by cans » Tue Jun 14, 2011 3:27 am
total 12W,10M
to select: 10W,8M
select those particular 2 men and 2 women.
Remaining: 10W,8M
to select:8W,6M
no. of ways = 10C8*8C6 = 10*9*8*7/4 =1260
IMO E
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