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Question

# A boat's crew consists of 8 men, 3 of whom can only row on one side and 2 only on the other. Let the number of ways in which the crew can be arranged be K3 .Find K ?

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Solution

## Let the men P,Q,R,S,T,U,V,W and suppose P,Q,R remain only on one side and S,T on the other as represented in the first 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 of S,T; 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, way, say that in which U is on the side of P,Q,R as shown in the second figure.Now P,Q,R,U can be arranged in 4 ways and S,T,V,W can be arranged in 4! ways. Hence total no. pf ways arranging the men=4!×4!=576Hence the number of ways of arranging the crew=3×576=1728∴K=12

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