Staying on the topic of probability, suppose you want to figure out the probability of drawing a certain 5 card poker hand. Sometimes we can list and the possible outcomes, but in this case it's virtually impossible to list all the 5 card hands that can be drawn from a standard 52 card deck. So we use combinations to solve such a problem. The number of possible 5 card hands that can be dealt from 52 cards if order is not important is 52!/(5! 47!) Recall that 52! = 52 * 51 * 50 *..... *1.

52!/(5! 47!) can be simplified to (52 * 51 * 50 * 49 * 48)/(5 * 4 * 3 * 2) = 2,598,960. That's how many possible 5 card hands can be dealt.

Then we just figure out the number of ways the certain hand you are looking for can be dealt and divide that by 2,598,960 to obtain the probability of obtaining such a hand.

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