Question

18. This is an excellent exercise for practicing counting. Find the number of f hands, dealt from a standard 52-card deck, that contain: (a) a royal flush (A-K-Q-J-10 all in one suit); (b) a straight flush (five cards of consecutive denominations all in one suit, but not royal flush); (c) four-of-a-kind (four cards of one denomination and one card of a different de nomination); (d) a full house (three cards of one denomination and t two of a different denomina tion); (e) a flush (five cards all in one suit, but not a straight flush or royal flush); (0) a straight (five cards of consecutive denominations, but not all in one suit); (8) three-of-a-kind (three cards of one denomination, a fourth card of a different denomination, and a fifth card of a third different denomination); (h) two pairs (two cards of one denomination, two cards of a different denomination, and a fifth card of a third different denomination); (i) one pair (two cards of one denomination, a third card of a different denomina- tion, a fourth card of a third different denomination, and a fifth card of a fourth different denomination); and G) none of the above. Compute the likelihood, or probability, of receiving each type of hand on the initial deal. (As a check, they are listed in increasing order of likelihood)

Answer 1