# 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.

(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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