12/23/2023 0 Comments Probability of drawing 5 cardsKeep in mind that there are 4 suits this can happen in, but we only want 1, and so we need to multiply by #C_(4,1)#. We're going to calculate all hands that involve a flush (so not just a flush but also a straight flush and royal flush) so that we'll be looking at any hand that has five cards of the same suit (with a suit having 13 cards in total). #C_(n,k)=(n!)/((k)!(n-k)!)# with #n="population", k="picks"#įirst let's calculate the denominator (picking 5 random cards from a pack of 52 cards): To find the probability, we need to find the fraction where the numerator is the number of ways to have a flush and the denominator is the number of 5 card hands possible.Įach of these numbers will be found using Combinations (we don't care about the order of the draw, merely of what ends up in our hand).
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