Question

No. of ways of dividing 80 cards into 5 equal groups of 16 each is

• A. $\frac{80!}{(16!{)}^5}$
• B. $\frac{80!}{(5!{)}^{16}}$
• C. $\frac{80!}{(5!{)}^5}$
• D. $\frac{80!}{(16!{)}^5.5!}$

Answer 1

The correct option is D $\frac{80!}{(16!{)}^5.5!}$

We can answer this problem in the following way

First choose 16 cards out of 80, next 16 cards out of (80-16), next 16 cards out of (80-32), and so on till 16 out of 16.

$\therefore$ total number of ways of doing this ${=}^{80}{C}_{16}{\times }^{64}{C}_{16}{\times }^{48}{C}_{16}{\times }^{32}{C}_{16}{\times }^{16}{C}_{16}$$=\frac{80!}{16{!}^5}$

But all the groups are equal so the permutations among them should not be included

$\therefore$ The answer is $=\frac{80!}{(16!{)}^5\times 5!}$