Poker can be played with hands of seven cards Calculate the

Poker can be played with hands of seven cards. Calculate the number of ways each of the following hands can be dealt from a standard 52 card deck. The order of the cards in your hand does not matter. For your answers to these questions, you may use the combination symbol, n C m , along with the standard mathematical operations (including factorial). Do not simplify your answers.

(a)Four-of-a-kind and a pair

(b) Four-of-a-kind

(c) Two three-of-a-kinds

(c) Three pairs

Solution

a) number of possible ways of AAAABBC = (13C1 * 4C4) *(12C1 *4C2) *(11C1*4C1) =41184

b) number of possible ways of AAAABCD = (13C1 * 4C4) *(12C3 *(4C1)^3 = 183040

c) number of possible ways of AAABBBC = (13C1 * 4C3) *(12C1 *4C3) *(11C1*4C1) =109824

d) number of possible ways of AABBCCD = (13C3 * 4C2 *4C2*4C2) *(10C1*4C1) = 2471040