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
= [tex]$^{13} C_2 \times ^{11} C_2 \times ^{9} C_2$[/tex]
[tex]$= \frac{13 !}{11 ! \times 2!} \times \frac{11 !}{9 ! \times 2!} \times \frac{9 !}{7 ! \times 2!} $[/tex]
[tex]$=\frac{13 !}{7! \times 2! \times 2! \times 2!}$[/tex]
= 120 number of ways
