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A club has 8 male and 8 female members. The club is choosing a committ

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Bunuel
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A club has 8 male and 8 female members. The club is choosing a committ [#permalink] New post   05 Nov 2017, 01:49
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A club has 8 male and 8 female members. The club is choosing a committee of 6 members. The committee must have 3 male and 3 female members. How many different committees can be chosen?

(A) 112,896
(B) 3,136
(C) 720
(D) 112
(E) 9
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B
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Re: A club has 8 male and 8 female members. The club is choosing a committ [#permalink] New post   05 Nov 2017, 02:32
Bunuel wrote:
A club has 8 male and 8 female members. The club is choosing a committee of 6 members. The committee must have 3 male and 3 female members. How many different committees can be chosen?

(A) 112,896
(B) 3,136
(C) 720
(D) 112
(E) 9


Since there are 8 male and female members
and we need to choose 3 members each for the committee,

we could choose them as follows: \(8c3*8c3 = 56^2 = 3136\)(Option B)
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Re: A club has 8 male and 8 female members. The club is choosing a committ [#permalink] New post   13 Sep 2020, 07:07
Bunuel wrote:
A club has 8 male and 8 female members. The club is choosing a committee of 6 members. The committee must have 3 male and 3 female members. How many different committees can be chosen?

(A) 112,896
(B) 3,136
(C) 720
(D) 112
(E) 9


Since it is a selection problem so we need to use "combination" formula.
(8 C 3) x (8 C 3)= 3136

I did a mistake of multiplying 2 times (8 C 3) which gave answer as 112 :(..
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Re: A club has 8 male and 8 female members. The club is choosing a committ [#permalink] New post   13 Sep 2020, 13:40
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Bunuel wrote:
A club has 8 male and 8 female members. The club is choosing a committee of 6 members. The committee must have 3 male and 3 female members. How many different committees can be chosen?

(A) 112,896
(B) 3,136
(C) 720
(D) 112
(E) 9


We need to choose 3 males out of 8, and 3 females out of 8. Then we have 8C3 options for males and females, multiply them to get the total possible amount of options.

8C3 * 8C3 = \((\frac{8 * 7 * 6 }{ 3!})^2 = (8*7)^2 = 56^2\).

We know \(50^2 = 2500\) so our answer should be somewhat comparable to that, then B is the closest option.

Ans: B
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Re: A club has 8 male and 8 female members. The club is choosing a committ [#permalink] New post   16 Jan 2024, 23:05
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Re: A club has 8 male and 8 female members. The club is choosing a committ [#permalink]
16 Jan 2024, 23:05
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