When playing a card game and seven cards are drawn, what is the probability of getting a 10, a Jack, a Queen and a King in the same suit?

Answer 1

There is only one way of getting 10, J, Q, K in one suit and there are 4 suits, i.e. 4 ways of getting the required cards. There are ₄₈C₃ ways of picking the other 3 cards. There are ₅₂C₇ equally likely ways of picking 7 cards from 52. The probability you want is 4 * ₄₈C₃ / ₅₂C₇. _nC_r is the binomial coefficient of picking r things from n.