Question

The number of ways in which 12 balls can be divided between two friends, one receiving 8 and the other 4, is

• A. $\frac{12!}{8!4!}$
• B. $\frac{12!2!}{8!4!}$
• C. $\frac{12!}{8!4!2!}$
• D. $\frac{12!}{4!}$

Answer 1

Answer: (B)

$\frac{12!2!}{8!4!}$

Number of ball is 12.
Hence required number of ways $=$ first one get 8 balls and second receives 4 ballss or vice versa .${=}^{12}{C}_8{.}^4{C}_4{+}^{12}{C}_4{.}^8{C}_8=2!{.}^{12}{C}_8=\frac{12!2!}{8!4!}$