Question

discrete structure

Recall that a standard deck of 52 cards has 4 suits (hearts, diamonds, spades, and clubs), each of which has 13 ranks: 2-10, Jack, Queen, King, and Ace (in order from lowest to highest). Order of cards in a hand does not matter (a) (10 points) A full house is 3 cards of one rank and 2 of another rank. How many full houses are there in a 5-card hand if either the pair or the 3 of a kind must be aces? (b) (10 points) A flush consists of 5 cards of the same suit. How many flushes are possible in a 5-card hand if the 2 of diamonds is missing from the deck? (c) (10 points) Assume you are dealt a hand that includes a pair of sixes, a 3, a Jack, and a 7. If you are playing against one other player, what is the probability they have a better pair? You may include hands that are better than a single pair (eg four of a kind, two pair, flush), as long as they include a higher pair than sixes

Answer 1

Solution ho us es in given of fale (a) To tal no uses with of full ho situ ahom ef fall no. + aces with 3 aces ho uses f) (4 x12 + x 12 X1 576 wayo 288 ナ 288 (b) total flushes to tal flusher 3 cOmplatt suts +fhshes fom diamond (1565 * 3) 130 + 3861 t 462 4323