Question

If 3n different things can be equally distributed among 3 persons in k ways then the number of ways to divide the 3n things in 3 equal groups is

• A. $kx3!$
• B. $\frac{k}{3!}$
• C. ${(3!)}^k$
• D. none of these

Answer 1

The correct option is B $\frac{k}{3!}$

Given, 3n different things can be equally distributed among 3 persons in k ways
For dividing 3n things between 3 persons equally, first we can make them into 3 different groups and then arrange them between 3 persons which can be done in 3! ways
But, given is it is equal to k
$\therefore$ number of ways to divide the 3n things in 3 equal groups$\times 3!=k$
$\therefore$ number of ways to divide the 3n things in 3 equal groups $=\frac{k}{3!}$