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# Groups P, Q, and R have 20 persons each, while group S has 10 persons.

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Math Expert
Joined: 02 Sep 2009
Posts: 58340
Groups P, Q, and R have 20 persons each, while group S has 10 persons.  [#permalink]

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02 Oct 2018, 01:54
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:50) correct 12% (01:53) wrong based on 47 sessions

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Groups P, Q, and R have 20 persons each, while group S has 10 persons. Groups P, Q, R, and S have no persons in common. A task force is to be formed by selecting one person from each of groups P, Q, and R and two persons from group S. How many different task forces are possible?

(A) 72,000
(B) 152,000
(C) 200,000
(D) 240,000
(E) 360,000

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Intern
Joined: 06 Nov 2014
Posts: 17
Location: Viet Nam
GMAT 1: 720 Q50 V36
GMAT 2: 740 Q50 V40
GPA: 3.67
Re: Groups P, Q, and R have 20 persons each, while group S has 10 persons.  [#permalink]

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02 Oct 2018, 02:08
A combinatoric problem.

There are 20 options to select a person from group P
There are 20 options to select a person from group Q
There are 20 options to select a person from group R
There are 10!/(2!*8!) = (9*10)/2 options to select a person from group S

Total number of possible task forces
= 20*20*20*9*10/2
= 10*20*20*90
= 360,000
Intern
Joined: 25 Sep 2018
Posts: 2
Re: Groups P, Q, and R have 20 persons each, while group S has 10 persons.  [#permalink]

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02 Oct 2018, 02:39
1
1
Applying combinations- ways of choosing y from x

P*Q*R*S= 20C1*20C1*20C1*10C2= 20*20*20*45 = 360,000 (E)
Re: Groups P, Q, and R have 20 persons each, while group S has 10 persons.   [#permalink] 02 Oct 2018, 02:39
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