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

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

=
`$^(13) C_2 * ^(11) C_2 * ^(9) C_2$`

`$= (13 !)/(11 ! * 2!) * (11 !)/(9 ! * 2!) * (9 !)/(7 ! * 2!) $`

`$=(13 !)/(7! * 2! * 2! * 2!)$`

= 120 number of ways