Question

4. In a 52 card deck there are 13 cards (2, 3, 4,5 6, 7, 8, 9,10,J Q, K A) in each of four suits (4, ◇〇4) (a) In how many different ways can you pick four cards with different suits? (b) In how many different ways can you pick four cards of the same suit? (c) In how many different ways can you pick four cards so that you have exactly three suits in your hand? (d) In how many different ways can you pick four cards so that your cards have exactly two distinct suits?

Answer 1

a)

13^4

since there are 13 cards in each suits

hence for each suits, there are 13 options

b)

13C4 * 4

we can choose particular suit by 4 ways as there are 4 options for suit

now for particular suit, there are 13C4 ways to choose 4 cards out of 13

hence

4*13C4

= 2860