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# A boat has a crew of eight; two of those eight can row only

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Manager
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A boat has a crew of eight; two of those eight can row only [#permalink]

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06 Mar 2006, 17:32
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A boat has a crew of eight; two of those eight can row only on the stroke side, while 3 can row only on the bow side. in how many ways can the two sides of the boat be manned?
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06 Mar 2006, 23:25
is it 12..

2 on one side and 3 on the other side.. Number of ways three people can be arranged is 3! and for each arrangement we need to look at two people on the other side. Therefore 3*2*2

It also says there are 8 crew members.. so i dont know where/how to use the rest 3.. is it irrelevant information??
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08 Mar 2006, 14:21
Is it 288?
2! * 3! * (3! + 3! + 3P2 + 3P2) = 288.
If we knew how many people were there on each side, it would be simpler.
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08 Mar 2006, 14:57
I think you have made a small mistake in calculation.
it should be 3 * 2 * 3! => 3 * 2 * 3*2 = 36

bewakoof wrote:
is it 12..

2 on one side and 3 on the other side.. Number of ways three people can be arranged is 3! and for each arrangement we need to look at two people on the other side. Therefore 3*2*2

It also says there are 8 crew members.. so i dont know where/how to use the rest 3.. is it irrelevant information??
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09 Mar 2006, 10:27
Do we assume that there needs to be 4 on each side? Then only 3 people can be on either side. So 6 ways to arrange the 3 people????

What's the OA?
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20 Mar 2006, 19:53
Late.
But I'll try.
2 sides of the boat-side 1 and side2
fix 3 people on side 1.
fix 2 people on side 2.
3 people remain.
2 people can go to side 1 in 3P2 = '3' ways
The remaining person can go to side 2 in '1' way only.
after assigning the team on either sides, the 2 sides can be rearranged amongst themselves in '4!' ways on 1 side and '4!' ways on the other side.
So, the total number of ways are
3*1*4!*4! = 1728.

Thanks,
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20 Mar 2006, 22:53
sorry I forgot to give the OA before

is 3c2 * (4!)^2

so is 1728 indeed, well done Gmate
20 Mar 2006, 22:53
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# A boat has a crew of eight; two of those eight can row only

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