Question

The number of ways in which a pack of 52 cards of four different suits can be distributed equally among four players so that each player gets the Ace, King, Queen and Knave of the same suit is

• A. $\frac{36!4!}{(9!)^{4}}$
• B. $\frac{36!}{(9!)^{4}(4!)}$
• C. $\frac{52!4!}{(9!)^{4}}$
• D. None of these

Answer 1

Answer: (A)

$\frac{36!4!}{(9!)^{4}}$

Answer 2

There are 16 (= 4 × 4) cards of Ace, King, Queen and Knave

These 4 sets of cards can be distributed in 4! Ways.

The remaining 36 cards are distributed among players and each player will get 9(= 36/4) cards. No. of ways of distributing these cards

= No. of ways of distributing these cards

= ³⁶C₉ × ^36–9C₉ × ^36–18C₉ × ^36–27C₉

= $\frac{36!}{9!27!}$×$\frac{27!}{9!18!}$×$\frac{18!}{9!9!}$×$\frac{9!}{9!0!}$=$\frac{36!}{(9!)^{4}}$

\ Total no. of ways = 4! × $\frac{36!}{(9!)^{4}}$ = $\frac{36!4!}{(9!)^{4}}$.