Question

The number of ways can a pack of 52 cards be divided into 4 sets, three of them having 17cards each and fourth just one card is

• A. $\frac{52!}{(17!{)}^3}$
• B. $\frac{52!}{3.(17!{)}^3}$
• C. $\frac{52!}{3!(17!{)}^3}$
• D. $\frac{52!}{3{!}^3(17!)}$

Answer 1

The correct option is C $\frac{52!}{3!(17!{)}^3}$

Required number of ways ${=}^{52}{C}_{17}{\times }^{35}{C}_{17}{\times }^{18}{C}_{17}{\times }^1{C}_1\times \frac{1}{3!}=\frac{52!}{3!(17!{)}^3}$
$3!$ is included since there is no distinction between those $3$ sets