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At a conference, one team is made up of 4 men and 5 women. Four presen

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At a conference, one team is made up of 4 men and 5 women. Four presen [#permalink]

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New post 04 Oct 2010, 21:12
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Question Stats:

82% (01:30) correct 18% (02:01) wrong based on 55 sessions

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At a conference, one team is made up of 4 men and 5 women. Four presenters are chosen to present the team's findings in front of the entire conference. How many different groups of presenters can be chosen from the team if a team cannot be composed of men only or women only? (Two groups of presenters are considered different if at least one presenter is different.)

(A) 120
(B) 126
(C) 180
(D) 420
(E) 460


Any quick way to solve this? I only solve it by splitting to 3 different scenarios. Takes way too much time.
[Reveal] Spoiler: OA

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Re: At a conference, one team is made up of 4 men and 5 women. Four presen [#permalink]

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New post 04 Oct 2010, 22:08
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rafi wrote:
At a conference, one team is made up of 4 men and 5 women. Four presenters are chosen to present the team's findings in front of the entire conference. How many different groups of presenters can be chosen from the team if a team cannot be composed of men only or women only? (Two groups of presenters are considered different if at least one presenter is different.)

(A) 120
(B) 126
(C) 180
(D) 420
(E) 460


Any quick way to solve this? I only solve it by splitting to 3 different scenarios. Takes way too much time.


No of ways = All ways to choose - ways using just men - ways using just women = C(9,4)-C(5,4)-C(4,4) = 126 - 5 - 1 = 120

Answer is (A)
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Re: At a conference, one team is made up of 4 men and 5 women. Four presen [#permalink]

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New post 05 Oct 2010, 08:14
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i got A. but i think i did it the long way.

if we want at least 1 sex per group, then we can have
3 women, 1 man
3 men, 1 woman
2 women, 2 men

3 women, 1 man = 5C3 * 4C1 = 40
3 men, 1 woman = 4C3 * 5C1 = 20
2 women, 2 men = 5C2 * 4C2 = 60

40 + 20 + 60 = 120 total
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Re: At a conference, one team is made up of 4 men and 5 women. Four presen [#permalink]

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New post 30 Jul 2017, 09:34
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Re: At a conference, one team is made up of 4 men and 5 women. Four presen   [#permalink] 30 Jul 2017, 09:34
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