A boat is to be manned by eight men, of whom 2 can only row on bow side and 1 can only row on stroke side; in how many ways can the crew be arranged?

Answer

1728

Explanation

Let the man P,Q,R,S,T,U,V,W and suppose P,Q,R remain only on one side and S,T one the other as represented in figure.

Then, since 4 men must row on each side, of the remaining 3, one must be placed on the side of P,Q,R and the other two on the side S,T and this can evidently be done in 3 ways, for we can place any one of the three on the side of P,Q,R.
Now, 3 ways of distributing the crew let us first consider one, say that in which U is on the side of P,Q,R as shown in figure.

Now, P,Q,R,U can be arranged in 4! ways ad S,T,V,W can be arranged in 4! ways. hence, total number of ways arranging the men`=4!=4!=576`
hence, the number of ways of arranging the crew
`=3xx576`
`=1728`