Question

The number of ways of distributing 3 dozen fruits (no two fruits are identical) to 9 persons such that each gets the same number of fruits is

• A. $\frac{36!}{(9!)^4}$
• B. $\frac{36!}{(4!)^9}$
• C. $^{36}P_9 \times 4!$
• D. $\frac{36!}{4!(9!)^4}$

Hint:

When distributing distinct items equally among groups, use multinomial coefficients considering identical group sizes.

Answer 1

The Correct Option is B

We have 36 distinct fruits to be distributed to 9 persons equally, so each person gets $\frac{36}{9} = 4$ fruits. Number of ways to distribute distinct fruits equally is the multinomial coefficient: \[ \frac{36!}{(4!)^9}. \] Thus, option (2) is correct.