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  4. 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, the number of ways in which the crew can be arranged is

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Q. 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, the number of ways in which the crew can be arranged is

Permutations and Combinations

Solution:

First we have to select 2 men for bow side and 3 for stroke side. The number of selections of the crew for two sides $= ^5C_2 × ^3C_3$
For each selection there are 4 persons on both sides, who can be arranged in 4! × 4!ways.
Required number of arrangement $= ^5C_2 × ^3C_3 × 4! × 4! = 5760$