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 person will not go in the same boat is

• A. $\frac{1}{2}\left( 10C_{5} \right)$
• B. 2$\left( 8C_{4} \right)$
• C. $\frac{1}{2}\left( 8C_{5} \right)$
• D. None of these

Answer 1

Answer: (B)

2$\left( 8C_{4} \right)$

Answer 2

First omit two particular persons, remaining 8 persons may be 4 in each boat. This can be done in ⁸C₄ ways. The two particular persons may be placed in two ways one in each boat. Therefore total number of ways are = 2 x ⁸C₄.