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Permutations / Combinations

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Permutations / Combinations

by anshul12089 » Wed Apr 20, 2011 3:15 pm
Can anyone please help me with this?

The crew of an 8 member rowing team is to be chosen from 12 men, of which 3 must row on on side only and 2 must row on the other side only. Find the number of ways of arranging the crew with 4 members on each side.

A)40,320
B)30,240
C)60,480
D)10,080
E)None of These
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by Anurag@Gurome » Thu Apr 21, 2011 9:05 pm
anshul12089 wrote:Can anyone please help me with this?

The crew of an 8 member rowing team is to be chosen from 12 men, of which 3 must row on on side only and 2 must row on the other side only. Find the number of ways of arranging the crew with 4 members on each side.

A)40,320
B)30,240
C)60,480
D)10,080
E)None of These
According to the given info, we have already selected 3 persons to row on side 1 and 2 to row on the side 2. So, we need to select 1 person for side 1 and 2 persons for side 2 from 7 persons left.
So, 1 person for side 1 and 2 persons for side 2 can be selected in 7C1 × 6C2 = 7 × (6 × 5)/2 = 105 ways.
Therefore, the number of ways of arranging the crew with 4 members on each side = 105 × 4! × 4! = 60,480

The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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