how do you solve card counting problems?how many sets of 7 cards are possible if you draw them from a reg.deck

Answer 1

Problems like this, where values cannot repeat, are a branch of Combinatorics known as choose problems. The basic part of a choose problem is NcX, which reads as "N choose X." This is often written as a set of parentheses with N and X in the middle, N over X.
NcX = N!/((N-X)!*X!)
So in the case of drawing seven cards from a regular deck, you're answer would be 52c7 = 52!/(45!*7!) = 52*51*50*49*48*47*46/7!
=133,784,560

If you drew seven cards, but replaced each card after you drew it (in other words values could repeat because you could conceivably draw the same card twice), then there would be 52^7=1,028,071,702,528 possible combinations. That would not be a choose problem because values could repeat.

Answer 2

Since there are 52 cards in a 'standard' deck, you cna choose 7 of them in
52!/((7!*(45!)) = 133,784,560 possible ways.


Doug