how many ways to deal one card to 6 people from a collection of 6 packs shuffled together? How many ways to deal one card to 6 people from a collection of 6 packs shuffled together?
each pack has 52 cards?
 A: If we consider all 312 cards distinguishable, then the number of ways is P(312,6) = $\frac{312!}{306!}$.
If cards of the same suit and rank are not distinguishable, then each person can get one of 52 cards, so there are $52^6$ possibilities.  However, note that the possibilities do not all occur with the same probability.
A: I’m assuming that cards of the same suit and rank are indistinguishable even if they’re from different decks. Note that there are enough decks so that every person can get the same card. Thus, every sequence of $6$ cards is possible: the first person can receive any of the $52$ distinct cards, the second can still receive any of the $52$ distinct cards, and so on all the way through the sixth person. There are therefore $52^6$ possible outcomes.
The question would be a little harder if only $5$ decks were shuffled together, because then the outcomes in which every person gets the same card would be impossible. However, those would be the only impossible outcomes, and there are just $52$ of them, so the problem wouldn’t be much harder: there would be $52^6-52$ possible outcomes.
