What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these Four cards are of the same suit? For cards are face cards? Cards are of the same colour? Four cards belong to four different suits? Two aqre red cards and two are black cards?

Explanation

number of ways of choosing 4 cards from a pack of 52 playing cards

`=\ ^{52} c_{4}=frac{52 !}{41 times 481}=frac{52 times 51 times 50 times 49 times 48 !}{4 times 3 times 2 times 48!}`

`=13**17**25**49`

`=270725`

(i)Four cards are of the same suit

`=4 times \ ^13 c_4=4 times frac{13 !}{4 ! times 9 !}`

`=13 times 2 times 11 times 10`

`=26 times 110`

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