Question

What is the number of ways of choosing 4cards from a bag of 52 playing cards ? In how many of these :

1) 4 cards are of the same suite

2) 4 cards belong to 4 different suites

3) 4 cards are face cards

4) two are red cards and two are black cards

Answer 1

total no. of ways for chosing 4 cards from 52 cards= 52c4
=270725.

in this;
1.If all the cards are of the same suit, then since there are four suits in a deck, then the number is 4 x 13C4 = 4 x ( 13 x 12 x 11 x 10 ) / ( 4! ) = 2860.

2.If the cards are to be of different suits ,then the number of combinations would be

13 x 13 x 13 x 13 = 28561

3. 3 cards are face cards
Jack,Queen,king are the face cards.
total no. of face cards=4×3=12 in all 52 cards
so no. ways=12c4=495.

4. chosing 2 red card=26c2
chosing 2 black card=26c2
no. ways for the combination=26c2×26c2
=105625