SOLUTION: A boat is to b manned by 8 men,of whom,one cannot row on the bow side and two cannot row on the stroke side. In how many ways can the crew be arranged?

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Question 891927: A boat is to b manned by 8 men,of whom,one cannot row on the bow side and two cannot row on the stroke side. In how many ways can the crew be arranged?
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
We will label the 1 man who cannot row on the bow side S, 
since he must row on the stroke side.

We will label the 2 men who cannot row on the stroke side B, 
since they must row on the bow side.

We will label the other 5 men BS, since they can row on
either side.

So the men are labeled:

S,B,B,BS,BS,BS,BS,BS

So the boat is manned this way:

Bow side:       B,B,BS,BS
Stroke side:    S,BS,BS,BS

We choose 2 BS's for the bow side in C(5,2) = 10 ways,
and the other three will be on the stroke side.

For each of those choices there are 4! or 24 ways to rearrange
the men on the bow side, and 4! or 24 ways to rearrange the men
on the stroke side.  

Answer: C(5,2)*4!*4! = 10*24*24 = 5760 ways.

Edwin
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