How many ways are there to deal five cards to six players from a deck of 48 distinct cards?
I know that $13^4 * 48$ divided by 2 (to remove duplicate hands) is the total number of possible 5 cards hands. I have no idea how to apply it to six people however. Any help would be greatly appreciated thanks!
There are $48!/18!$ ways you can pick 30 cards to be dealt to the six players (48 ways for the first card, 47 for the second, ... down to 19 ways for the last of the cards). Let the first five of the cards be for the first player, the second five of the cards be for the second player, and so on for each of the six players. However, a player has the same hand regardless of the order of his/her five cards, so you must divide by 5! for each of the six players.
${48! \over (48 - 5 \cdot 6)! (5!)^6} = 649352163073816339512038979194880$.