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Tue October 30, 2012 By: Megha M
What is the no. of ways of choosing 4 cards from a pack of 52 playing cards? In how many ways if these 1. 4 cards are of the same suit 2.4 cards belong to 4 different suits 3. All are face cards 4. 2 are red cards and 2 are black cards 5. Cards are of the same colour
Expert Reply
Number of ways of choosing 4 cards from a pack of 52 playing cards is ^{52}C_{4} .
The number of ways to choose four cards ofthe same suit is ^{4}C_{1}^{13}C_{4}. In this computation, we first choose which one suit of the 4 available, then choose the 4 cards out of the 13 available in that suit.
The number of ways to choose four cards of four different suits is ^{4}C_{4 }(^{13}C_{1})^{4}. Here, we chose the four suits all at once, then for each suit, identified, choose one of the 13 cards.
Similarly, you can find the number of ways in the other cases.
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