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Out of 8 sailors on a boat, 3 can work o...

Out of 8 sailors on a boat, 3 can work only on one particular side and 2 only on the other side. Find the number of ways in which the sailors can be arranged on the boat.

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The correct Answer is:
1728
Let the particular side on which 3 particular sailors can work be named A, and another side B on which 2 particular sailors can work. Thus, we are left with 3 sailors only.
The number of ways of selection of one sailor for side A is `.^(3)C_(1)=3` and then we are left with 2 sailors for other sides. Now, on each side 4 sailors can be arranged in 4! ways. Hence, total number of arrangements is `3xx4!xx4!=3xx24xx24=1728`.
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