in how many ways a pack of 52 playing card be distributed equally to groups of 4 set?

Anoopam Mishra
126 Points
7 years ago
First chose 13 cards out of these 52 cards and give it to the first player.
Number of ways = $_{13}^{52}\textrm{C}$
Then chose 13 cards out of the remaining 39 cards and give it to the second player.
Number of ways = $_{13}^{39}\textrm{C}$
Then chose 13 cards out of the remaining 26 cards and give it to the third player.
Number of ways = $_{13}^{26}\textrm{C}$
Finally give the remaining cards to the fourth player.
Number of ways = $_{13}^{13}\textrm{C}$ = 1
So number of ways of distributed the 52 cards = $_{13}^{52}\textrm{C} \ * \ _{13}^{39}\textrm{C} \ *\ _{13}^{26}\textrm{C}$ = $\frac{52!}{(13!)^4}$