Picking 4 cards out of a deck of 52 what is the probability of picking 3 from one suit and 1 from another suit?

To determine the probability of picking 3 cards of one suit and 1 card of another in a standard 52 card deck, consider each card one at a time.

The probability of picking a card in any suit is 52 in 52, or 1.

Since there are now only 12 cards in the first suit, the probability of picking a card in the same suit is 12 in 51, or 4 in 17, or 0.2353.

Since there are now only 11 cards in the first suit, the probability of picking a card in the same suit is 11 in 50, or 0.22.

Since there are still 39 cards in the remaining three suits, the probability of picking a card in a suit different than the first is 39 in 49, or 0.7959.

The probability of picking 3 cards of one suit and 1 card of another in a standard 52 card deck is, therefore, the product of the probabilities of each card, or (52 in 52) (12 in 51) (11 in 50) (39 in 49), or 267696 in 6497400, or 0.0412, or about 1 in 25.