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jainvineet
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ps- probability - committee. 16 Oct 2005, 20:03
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A committee of 4 is to be picked from 6 men and 4 women. What is the probabilty that half of the commitee will be made up of women?



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ps- probability - committee. 16 Oct 2005, 20:42
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jainvineet
A committee of 4 is to be picked from 6 men and 4 women. What is the probabilty that half of the commitee will be made up of women?
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2 men chosen from 6 x 2 women chosen from 4/4 people chosen from a pool of 10


(6C2*4C2)/(10C4)=3/7
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jainvineet
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ps- probability - committee. 16 Oct 2005, 20:56
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Antmavel
(2C6*2C4)/(4C10) = 3/7
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Please explain why cant we have it like


6/10 * 5/9 * 4/8 * 3/7


probability of a man out of 10 and then a man out of 9 and so on.

This is the key thing I am not able to understand.
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ps- probability - committee. 16 Oct 2005, 21:06
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# of ways to pick 4 people from 10 = 10C4 = 10!/4!6! = 210 ways

# of ways to pick 2 women = 4C2 = 6
# of ways to pick 2 men = 6C2 = 15
Total number of ways that half of committe is women = 15*6 = 90

P = 90/210 = 3/7
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ps- probability - committee. 16 Oct 2005, 23:09
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jainvineet
Antmavel
(2C6*2C4)/(4C10) = 3/7

Please explain why cant we have it like


6/10 * 5/9 * 4/8 * 3/7


probability of a man out of 10 and then a man out of 9 and so on.

This is the key thing I am not able to understand.
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I am not a specialist but I think that the reason is because when you organize your calculation like you've suggested before, you're giving a precise order.
For example : 6/10*5/9*4/8*3/7 is ok, but don't you think that 4/10*6/9*3/8*5/7 is also correct ? of course the result will be the same but it's another way to get also half of the people to be women. When you use combinations you calculate all the possible ways to get a result.

Moreover, if you take some extra time you will see that there are 4W and 6M, we need 4 people, half men and half women. If there were 5W and 5M the probability would be 50% but now there are 4W and 6M so the probability to pick 2W and 2M should be a little lower. But 1/14 is not a realistic figure, it's too low :wink:
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ps- probability - committee. 17 Oct 2005, 08:33
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jainvineet
Antmavel
(2C6*2C4)/(4C10) = 3/7

Please explain why cant we have it like


6/10 * 5/9 * 4/8 * 3/7


probability of a man out of 10 and then a man out of 9 and so on.

This is the key thing I am not able to understand.
Show more


In your approach you would count ABCD as a different outcome from DCBA, while they are actually the same group of four people, just picked in different orders. If you do this then you need to divide your result by P(4,4).



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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Thank you for understanding, and happy exploring!
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