Question

The number of ways of dividing 52 cards amongst four players so that three players have 17 cards each and the fourth player just one card, is

• A.
• B. 52 !
• C.
• D.

Answer 1

The correct option is A

For the first set number of ways ${}^{52}{C}_{17}$. Now out of 35 cards left 17 cards can be put for second in ${}^{35}{C}_{17}$ ways similarly for $3^{rd}$ in ${}^{18}{C}_{17}$ One card for the last set can be put in only one way. Therefore the required number of ways for the proper distribution = $\frac{52!}{35!17!}\times \frac{35!}{18!17!}\times \frac{18!}{17!1!}\times 1!$ = $\frac{52!}{(17!{)}^3}$