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Question

A boats crew consists of 8 Men,3 of whom can only row on one side ,2 only on other .The number of ways the crew can be arranged is.

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Solution

With the following assumptions, answer is 17281728
(1) 4 persons must sit in each side (as normally equal number of persons sits in each side).
(2) arrangements of the persons within a particular side are different.

select the 3 persons who sit on first side(1 way).
select the 2 persons who sit on second side(1 way).

There are 3 persons remaining. Select one person from them for the first side(3C1=3 ways). Now total number of persons in the first side becomes 4.

Remaining 2 persons can be selected for the second side only in one way. Now total number of persons in second side also becomes 4.

4 persons in first side can be arranged in 4! ways.

4 persons in second side canbe arranged in 4! ways.

Required number of ways
=3×4!×4!=1728=3×4!×4!=1728


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