Answer to Question #145301 in Statistics and Probability for Shiwa n

Question

You have a deck of 52 playing cards
(i) How many different 5 card hands can be dealt?
(ii) What is the probability that a hand of 5 dealt randomly contains 3 aces?
(iii) What is the probability that a hand of 5 dealt randomly will have 5 cards of the same
suit?

Answer 1

Answer 1)

Total number of getting different 5 card hands from a 52 card deck = 52C5 = 2598960

Answer 2)

Probability of getting 3 aces in a 5 card hand = $\frac {4C3*48C2}{52C5} = \frac {4*1128}{2598960} = 0.001736$

Answer 3)

Probability of getting all 5 cards in a hand of same suit = $\frac {4*13C5}{52C5} = \frac {4*1287}{2598960} = 0.00198$