Question

The number of ways of distributing 50 identical things among 8 persons in which such a way that three of them get 8 things each, two of them get 7 things each and remaining three get 4 things each is equal to,

• A. $\frac{8!}{3!2!}$
• B. $\frac{8!}{{\left(3!\right)}^2.2!}$
• C. $\frac{50!8!}{{\left(3!\right)}^{2}2!}$
• D. $\frac{8!}{3!}$

Answer 1

The correct option is B $\frac{8!}{{\left(3!\right)}^2.2!}$

Arrangements are

8 8 8 4 4 4 7 7

Number of ways are=$\frac{8!}{3!\times 3!\times 2!\times 2!\times 2!}\times 2!=\frac{8!}{3!\times 3!\times 2!}$

(2! is because there are two 3! groups)