In a standard deck of cards (52 cards), how many different 5-card hands may be dealt in a game?

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This would be a variation on the Fundamental Counting Principle, where there are five categories and the number of possible outcomes in each category is determined by the total number of possible outcomes, less how many choices have been removed from “play” (by already being dealt)   So, there are 52 possible cards that can start the hand, buy only 51 will be available to provide the second, the third will come out of the remaining 50, and so on.  So, your result is 52 * 51 * 50 * 49 * 48 = 311,875,200 possible 5 card combinations in a 52 card deck.