Probability/Combinatorics
posted by Jay on .
If 4 cards are drawn at random from a standard deck of cards, what are the odds, or probability, that the first three will be of the same suit and the fourth of another suit?

First card: any card (52/52)
Second card: one of 12 remaining cards of the same suit (12/51)
third card: one of 11 remaining cards of the same suit (11/50)
fourth card: one of 39 cards of any other suit (39/49)
Since all these are required events, use the multiplication rule to get the combined probability of all four events happening.
Odds are P(E)/(1P(E)) where P(E) is the probability of an event taking place.