Odds of a card coming out

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I was wondering as to what the formula is to figure out what the odds are of certain cards coming out with x amount of players playing.
9 Players, chances of a 2 - A coming out
8 Players, chances of a 2 - A coming out
and so forth

It does not have to be suited. But if there is a formula to determine the chances of somebody holding two diamonds, etc... then that would be helpful

Thanks