probability homework question

[BruceZ]

[ QUOTE ]
anyone wanna help with some homework?? [img]/images/graemlins/smile.gif[/img]

What is the probability of getting 5 cards dealt (normal deck) and three of the cards are the same denomination (trips), and the other two cards are one above and one below...example: 8 8 8 9 7

thanks in advance!!

[/ QUOTE ]

Count the number of ways to make such a hand, without regard to the order of the cards, and divide by the total number of possible hands C(52,5) = 2,598,960. Consider the number of possible denominations for the set, the number of ways to make a set for each denomination, and the number of ways to get the other 2 cards. You need to know if the ace can be either a high or low card, and whether it can be both in the same hand. If it can be either high or low, but not both in the same hand, then AAA2K is not allowed, but 222A3 and KKKQA are both allowed, and the final answer comes to about 0.03%.