Deck of Cards Probability

Question

You pick 3 cards from a regular deck of 52 cards. Answer the following:

1. What is the probability that all three are Kings?
2. What is the probability they have all have different values (e.g. a 6, 8, and Jack)?

Answer 1

Pr(3 Kings in 3 draws) = (4/52)(3/51)(2/50) = .00018 = .018% chance of 3 Kings

Pr( 3 different cards) = (48/51) 48 ways not to match the 1st card, times ((50-6)/50

= (48/51)(44/50) = about 83% chance of all different values in 3 draws

44 ways to not match the 1st & 2nd card on the 3rd draw, 6 ways to match out of 50 remaining cards