Question
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
Thu November 01, 2012
Number of ways of choosing 4 cards from a pack of 52 playing cards is 52C4 .
 
The number of ways to choose four cards ofthe same suit is 4C113C4. 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 4C4 (13C1)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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