5. In how many ways can four men and five women be seated around a circular tabl

Question

5. In how many ways can four men and five women be seated around a circular table so that no two men are seated next to one another? (Note that two seating arrangements are considered to be the same if one can be obtained from the other by rotating the table.)


6. What is the probability that a five-card poker hand contains three of a kind? Two pair? (For those who may not play cards: A standard deck of fifty-two cards contains four cards each of thirteen denominations {2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A}. “Three of a kind” means three of the cards have the same denomination a, and the remaining cards have different denominations b and c. “Two pair” means the hand contains two cards each of two denominations and one card of a third denomination.)

Explanation / Answer

5. Your answer is here: http://answers.yahoo.com/question/index?qid=20100602181825AA6H7qs 6. three of a kind: http://www.mcs.sdsmt.edu/~ecorwin/cs251/t3s96sln/t3s96sln.html two of a kind: http://tiny.cc/owqwp (scroll down to EXAMPLE PROBLEMS)

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