Question

In how many ways 13 cards to each $4$ players to be distributed from a pack of $52$ cards & that each many have
(i)Ace, King, Queen, Jack of same suit
(ii)Ace, King, Queen, Jack of any suit

Answer 1

(i) First, a suit is chosen in ${}^4{C}_1$ ways.

Now, the Jack, Queen, King and Ace are removed and distributed in $4!$ ways.

Now, remaining 48 cards are distributed in 4 groups in $\frac{48!}{12!12!12!12!}$

$\therefore$ Total no. of ways$=4!\times 4\times \frac{48!}{12!12!12!12!}$

(ii) First Ace,Jack,King & Queen are chosen.

${}^4{C}_1{\times }^4{C}_1{\times }^4{C}_1{\times }^4{C}_1$ and distributed in $4!$ ways.

$\therefore$ Total no. of ways$=(4{)}^4\times 4!\times \frac{48!}{12!12!12!12!}$