Re: if you want to practice combinatorics: omaha question
(1) is easy. There are 40 cards dealt, the chance is 40/52 = 10/13 that one of them is A[img]/images/graemlins/spade.gif[/img].
(2) Once someone gets A[img]/images/graemlins/spade.gif[/img] there are C(51,3) = 20,285 possible ways to complete their hand. There are C(39,3) = 9,139 ways to complete the hand without another spade. So the chance is 1 - 9,139/20,285 = 56% that the hand has at least one other spade.
(3) Now there are 44 unknown cards (52 - 4 in your hand - 3 on the board - A[img]/images/graemlins/spade.gif[/img]) with 10 spades. So it's 1 - C(34,3)/C(44,3) = 5,984/13,244 = 55%.
(4) 1 - C(36,3)/C(44,3) = 7,140/13,244 = 46%.
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