# probability help

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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 by allthebest

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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

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