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

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

06 Mar 2006, 18:32

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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07 Mar 2006, 00:25

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, 15:21

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, 15:57

I think you have made a small mistake in calculation.
it should be 3 * 2 * 3! => 3 * 2 * 3*2 = 36

bewakoof wrote:

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09 Mar 2006, 11:27

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, 20:53

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, 23:53

sorry I forgot to give the OA before

is 3c2 * (4!)^2

so is 1728 indeed, well done Gmate

[#permalink] 20 Mar 2006, 23:53

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

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

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

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