Among 2598960 possible 5-card poker hands from a standard 52-card deck, how many contain the folowing cards?

Choose a card, it will be of some suit.

Chances of next card being same suit: 12 / 51

Next again: 11/50

Next: 10/49

Last: 9/48

12 * 11 * 10 * 9 / (51 * 50 * 49 * 48) =

11880 / 5997600 = .0019807 ... in poker terms 0.2% chance of a flush

Complementary probability = .99802 ... 99.802% chance of a non-flush,

i.e. more than one suit represented in 5 cards drawn at random

- - - If you want to use the given information:

13 C 5 = 5148 * 4 = 20592 / 2598960 to get the same result.

(Sets of 5 cards of any one suit * 4 suits)

.

easy. the prob to draw all the same suit is (13c5*39c0)/52c5

that is to pick one suite. you have four suites, so the answer times 4

that gives you 0.001981

compliment that is 0.998