Question

Number of ways in which a pack of $52$ playing cards be distributed equally among four players so that each have the Ace, King, Queen and Jack of the same suit, is

• A. $\frac{36!\cdot 4!}{(9!{)}^4}$
• B. $\frac{36!}{(9!{)}^4}$
• C. $\frac{52!\cdot 4!}{(13!{)}^4}$
• D. $\frac{52!}{(13!{)}^4}$

Answer 1

The correct option is A $\frac{36!\cdot 4!}{(9!{)}^4}$

Let Ace, King, Queen and Jack be one unit

Therefore ways of distributing these 4 units in 4 players will be 4!=24

And ways of distributing 36 cards wil be $\frac{36!}{{9!}^4}$

Since the cards should be distributed equally among 4 players

$\therefore Answer\Rightarrow \frac{36!\cdot 4!}{(9!{)}^4}$