Let's say that four of us (persons A, B, C, and I) are each handed our own, complete deck of cards. All four decks are identical, meaning that an Ace of Hearts in B's deck is equivalent to (and therefore, not unique from) an Ace of Hearts in mine.
We each draw nine cards at random from our own decks, and set them aside in our own, separate piles. To clarify, these cards are drawn without replacements, meaning that once we've each drawn our nine cards, we are each left with two piles: a stack of nine cards, and the original deck of cards, which now has forty-three cards remaining.
We then take these four piles of nine cards, and combine them into a single stack of thirty-six cards. After removing duplicates from the new stack, how many unique cards are we likely to have?