Probability Question

**Detanon** · May 29th 2010, 05:17 PM

A group of eight is to be chosen at random from eight men and six women.
What is the probability that
i. the group contains the same number of men and women?
ii. the group contains at most one woman?
iii. the group contains the oldest person but not the youngest person?

**SpringFan25** · May 29th 2010, 06:24 PM

there are no new concepts here from what you posted in

http://www.mathhelpforum.com/math-he...ability-q.html

If you are stuck please say exactly where, dont post your entire assignment on the forum in different threads

**Detanon** · May 31st 2010, 09:03 AM

Well heres what I did
(8 choose 4) x (6 choose 4) = 70 x 15 = 1050
(14 choose 8) = 3003

so the probability = 1050/3003.
I dont know if thats right though

**Archie Meade** · May 31st 2010, 10:16 AM

Originally Posted by Detanon

Well heres what I did
(8 choose 4) x (6 choose 4) = 70 x 15 = 1050
(14 choose 8) = 3003

so the probability = 1050/3003.
I dont know if thats right though

Yes, that's fine since any group of 4 men can go with any group of 4 women,
which is why the selections are multiplied.

(ii)

At most 1 woman is 1 woman or no women,
which means 1 woman and 7 men or all 8 men.

$P=\frac{\binom{8}{7}\binom{6}{1}+\binom{8}{8}\bino m{6}{0}}{\binom{14}{8}}$

(iii)

If the group contains the oldest person and excludes the youngest person,
then the oldest person can go with 7 of the remaining 12.

The number of ways this can happen is $\binom{12}{7}$

hence $P=\frac{\binom{12}{7}}{\binom{14}{8}}$

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