Question

You have to divide a pack of $52$ cards equally among $4$ players. In how many ways the cards can be divided in $4$ sets, $3$ of them having $17$ cards each & the $4^{th}$ with $1$ card

• A. $\frac{52!4!}{3!(17!{)}^3}$
• B. $\frac{52!}{(3!{)}^3(17!)}$
• C. $\frac{52!}{(3!)(17!)}$
• D. $\frac{52!}{(17!{)}^3}$

Answer 1

The correct option is A $\frac{52!4!}{3!(17!{)}^3}$

First select $17$ cards out of $52$ cards in ${}^{52}{C}_{17}$.

Then select $17$ from the remaining $35$ cards in ${}^{35}{C}_{17}$.

Then select $17$ again from the remaining $18$ in ${}^{18}{C}_{17}$ ways.

Total no. of ways

$=$ ${}^{52}{C}_{17}{\times }^{35}{C}_{17}{\times }^{18}{C}_{17}\times 1{\times }^4{C}_3$
$=$ $\frac{52!4!}{3!(17!{)}^3}$