For the probability of a full house, I did:
52/52 * 3/51 * 2/50 * 48/49 * 47/48 = 3/20825
I was off by a factor of 10 or in other words:
C(5,3)
Can anyone explain how to get this factor to me please?
2026-03-25 06:31:58.1774420318
Full House Probability: Why is my answer incorrect?
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You are assuming that the Full House, which is of the form $AAABB$ for some $A$ and $B$, is being dealt to you in that very order: i.e. that first you get all the three $A$'s, and then you get the two $B$'s. However, if the cards are being dealt to you in the order $BAABA$ you end up with the same Full House. Indeed, there are $5 \choose 3$ ways in which the three $A$'s are being dealt to you to get three $A$'s and two $B$'s.