Question

A boat crew consisting of $8$ men, $3$ of whom can only row on one side and $2$ only on the other. The number of ways in which the crew can be arranged is

• A. $1728$
• B. $1927$
• C. $1518$
• D. $2028$

Answer 1

Answer: (A), (C)

$1728$
$1518$

$4$ men must row each side
But on one side, there are already three men and on the other side two.
So one must be placed on the side of three men and two on the other side.
This can be done in ${}^3{C}_1$ or $3$ ways.
Again $4$ men on each side can be arranged among themselves in $4!$ ways
Hence, the required number of ways ${=}^3{C}_1\times 4!\times 4!=3\times 24\times 24=1728$