Question

In how many ways can 10 balls be divided between two boys, one receiving two and the other eight balls.

• A. 45
• B. 75
• C. 90
• D. None of these

Answer 1

Answer: (C)

90

Answer 2

$A$ gets 2, $B$ gets 8; $\frac{10\mspace{6mu}!}{2\mspace{6mu}!\mspace{6mu} 8\mspace{6mu}!} = 45$

$A$ gets 8, $B$ gets 2; $\frac{10\mspace{6mu}!}{8\mspace{6mu}!\mspace{6mu} 2\mspace{6mu}!} = 45$

$\therefore 45 + 45 = 90$.