At a conference, one team is made up of 4 men and 5 women. Four presen : GMAT Problem Solving (PS)
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# At a conference, one team is made up of 4 men and 5 women. Four presen

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Manager
Joined: 04 Jun 2010
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Concentration: General Management, Technology
Schools: Chicago (Booth) - Class of 2013
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Kudos [?]: 238 [0], given: 43

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

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04 Oct 2010, 21:12
00:00

Difficulty:

25% (medium)

Question Stats:

83% (02:19) correct 17% (01:19) wrong based on 12 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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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

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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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05 Oct 2010, 08:14
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] 05 Oct 2010, 08:14
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