Question

In a certain card game, only the thirteen cards that are Hearts are used, and each player is dealt a hand of just two cards. How many ways are there to deal hands of two cards each to each of three players from a 13-card deck comprised of just the Hearts?

Answer 1

Solution :

It is given that only 13 cards that are Hearts that is used in a certain game.

And 2 hearts to each of the 3 players.

Therefore, the number of ways is

= $^{13} C_2 \times ^{11} C_2 \times ^{9} C_2$

$= \frac{13 !}{11 ! \times 2!} \times \frac{11 !}{9 ! \times 2!} \times \frac{9 !}{7 ! \times 2!}$

$=\frac{13 !}{7! \times 2! \times 2! \times 2!}$

= 120 number of ways