Q. 314.8( 5 Votes )

What is the number of ways of choosing 4 cards from a deck of 52 cards? In how many of these,

(a) 3 are red and 1 is black.

(b) All 4 cards are from different suits.

(c) are face cards.

(d) All 4 cards are of the same suit.

Answer :

(a) 3 are red and 1 is black


Total ways = 26C3 × 26C1





= 2600 × 26


= 67600 ways


(b) All 4 cards are from different suits.


Total ways = 13C1 × 13C1 ×13C1 ×13C1


= (13C1)4





= 134


= 28561 ways


(c) are face cards.


There are 12 face cards.


So total ways = 12C4





= 495 ways


(d) All 4 cards are of the same suit.


As there are 4 suits.


Total ways = 13C4 +13C4 + 13C4 + 13C4


= 4× 13C4






= 2860 ways


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