Poker CombinationsHow many of each hand are there in a deck?

I Win by flickr user Kevin Labianco

(e) Flush [5 cards of the same suit but not in sequence, not including the straight flush and royal flush above]

(f) Straight [5 cards in sequence, but not all of same suit. Ace high or low]

(g) Three of a Kind [exactly 3 cards of one face value and 2 different cards]

(h) Two pairs [one pair of each two different face values and a card of a third face value]

(i) One pair [two of one face value, and 3 cards of different face values, no matching the pair]

(j) No pairs [5 different face values, not in sequence, not all cards in the same suit]

(3) Eight friends go to dinner. How many ways can they be seated at a circular table if three of them insist on sitting together?

(4) A multiple choice exam has 20 questions, each with four possible answers, and 10 additional questions, each with five possible answers. How many different answer sheets are possible?

(5) In a 52 card deck, how many 5 card poker hands are possible that have exactly two pair? one pair?