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

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

Grade:12th pass

1 Answers

Anoopam Mishra
126 Points
8 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}
 

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