What is number of ways of choosing 4 cards from a pack of 52 well shuffled cards:
a. four cards are of same suit
b.four cards are of different suit
c.are face cards
d.two are red cards and two are black cards
e.cards are of same color
a) one suit has 13 cards.
ways of choosing 4 cards from 13 cards = 13C4
probability of getting 4 cards of same suit = 13C4/52C4.
b) for all cards to be of different suits. you chose one card from each suit. you can do this in 13C1* 13C1 * 13C1* 13C1 ways.
probability = (13C1)^4/ 52C4.
c) there are 3 face cards in each suit.
that means 12 face cards in a deck of 52.
no. of ways of choosing 4 face cards from 12 such cards = 12C4
probability =12C4/ 52C4.
d) no. of red cards=26
no. of black cards=26
no. of ways of choosing 2 red and 2 black = 26C2*26C2
probability = (26C2*26C2)/52C4
e) no. of cards of same color= 26
no. of ways of choosing 4 cards from these 26 = 26C4
probability = 26C4/52C4.
hope it was helpful.
Added probability too, in case you'd need it