allthebest Posted May 2, 2016 Report Share Posted May 2, 2016 (edited) Help with this question: using a 52 card pack, a 'royal flush' consists of the 10, J, Q, K A of one suit. Find the probability of dealing: a. a royal flush in any order b. a royal flush in the order 10, J, Q, K, A ans: a. 1.54 x 10^-6 b. 1.28 x 10^-8 Edited May 2, 2016 by allthebest Reply Link to post Share on other sites More sharing options...
kw0573 Posted May 2, 2016 Report Share Posted May 2, 2016 a) P(RF, order does not matter) = combinations of royal flush of any of 4 suits / total dealing of 5 cards b) P(RF, order matters) = permutations of royal flush of any of 4 suits / total dealing of 5 cards nPk = permutations, nCk = combinations a) P(RF) = 4 * (1 combo / suit) / (52 C 5) = 1.54 * 10^(-6) b) P(RF) = 4 * (1 permutation / suit) / (52 P 5) = 1.28 * 10^(-8) Note that answer a) is answer b) times 5!, or 120, or the factor from 52 5 to 52P5 Reply Link to post Share on other sites More sharing options...
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