Discrete MathLogic These questions all relate to possible f

. Discrete Math/Logic

These questions all relate to possible five cards hands from a standard deck of 52 cards.Be sure to explain how you arrived at your answers.

Find the number of five card hands that have:

(a) 2 cards of one color and 3 of the other color

(b) All cards of the same color

(c) At least two queens

(d) A four flush is a poker hand consisting of four cards of one suit and a fifth card of another suit, but containing no pairs. How many possible four flushes are there?

(e) All face cards (Jack, Queen, King- can be different suits)

Solution

a) 2 cards of one color and 3 of the other color

= 2(26C2)(27C3)

b) 2(26C5)

c) 2 q, 3 others or 3 q, 2 others or 4 q, 1 other

4C2(48C3)+4C3(48C2)+4C4(48C1)

d) 4(13C4) ( 35C1)

e) 12C5