Question

The number of ways in which $10$ persons can go in two boats so that there may be $5$ on each boat, supposing that two particular persons will not go in the same boat?

• A. $\frac{1}{2}\left({}^{10}C_5\right)$
• B. $2\left({}^{8}C_4\right)$
• C. $\frac{1}{2}\left({}^{8}C_5\right)$
• D. None of these

Answer 1

The correct option is B

$2\left({}^{8}C_4\right)$

Explanation for the correct option(s)

Find the number of ways.

Consider the given data $10$ persons can go in two boats so that there may be $5$ on each boat,

The $2$ persons who don't want to go in same boat can be seated in each boat in $2$ ways

And the remaining $8$ persons can be seated by forming $2$ equal groups of $4$ persons in each boat and can be expressed as ${}^{8}C_4$.

Therefore, total number of ways $=2\left({}^{8}C_4\right)$

Hence Option B is correct