Latest MBA Aptitude Question SOLUTION: The crew of an 8 member rowing team is to be chosen fom 12 men, of which 3 must row on one side only and 2 must row on the other side only. Find the number of ways of arranging the

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(#M40015074) MBA question permutations and combinations, probability Keep an EYE

The crew of an 8 member rowing team is to be chosen fom 12 men, of which 3 must row on one 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.

1) 40320
2) 30240
3) 60480
4) 10080
5) None of these

Asked In MBA (11 years ago)

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Read Solution (1) :

Aman Priya  (8 years ago)

we have to select those 5 (3 +2) persons on whom there is a condition.
We need 4 members on each side of the both.
Since 3 members are already selected for one side and 2 for the other side we need to select 1 person to row on one side and 2 persons to row on the other side.
Eventhough there are 12 persons since we have already selected 5, we are left with another 7 persons
From these 7 persons I can select 1 person to row one side in 7C1 ways and from the remaining 6 persons I can select 2 persons for the other side in 6C2 ways.
Hence the required number of people can be selected in 7C1 x 6C2 = 105 ways.
Now look at the question carefully. If it is : In how many way can we accommodate the crew the answer will be 105
But in the question it is asked in how many can we arrange the crew.
Since there are 4 people on each side, we can arrange each team in 4! ways.
So we first select and then arrange.
Hence the answer will be 105 * 4! * 4! = 60480

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