Example: What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these
(i). four cards are of the same suit,
(ii). four cards belong to four different suits,
(iii). are face cards,
(iv). two are red cards and two are black cards,
(v). cards are of the same colour?
Solution: There will be as many ways of choosing 4 cards from 52 cards as there are combinations of 52 different things, taken 4 at a time. Therefore, The required number of ways
(i). There are four suits: diamond, club, spade, heart and there are 13 cards of each suit. Therefore, there are ways of choosing 4 diamonds. Similarly, there are ways of choosing 4 clubs, ways of choosing 4 spades and </sub> ways of choosing 4 hearts. Therefore, The required number of ways
(ii). There are 13 cards in each suit. Therefore, there are ways of choosing 1 card from 13 cards of diamond, ways of choosing 1 card from 13 cards of hearts, "C ways of choosing 1 card from 13 cards of clubs, ways of choosing 1 card from 13 cards of spades. Hence, by multiplication principle, the required number of ways
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(iii). There are 12 face cards and 4 are to be selected out of these 12 cards. This can be done in ways. Therefore, the required number of ways
(iv). There are 26 red cards and 26 black cards. Therefore, the required number of ways
(v). 4 red cards can be selected out of 26 red cards in ways. 4 black cards can be selected out of 26 black cards in ways .
How to calculate combinations of multiple item types?
Therefore, the required number of ways
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