Seven cards are selected at random from a standard deck of 52 cards, what is the probability there will be no pairs? (pairs means two cards of the same denomination and same color)
2026-03-31 07:07:13.1774940833
Seven cards are selected at random from a standard deck of 52 cards...
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$\textbf{Hint:}$ From your definition of pair (which is not the standard definition of what a pair is), each card only has one pair. Split the cards into $2$ decks, $26$ cards each, so that each card in deck $1$ has a pair in deck $2$. How many ways can you pick $7$ cards so that there are no pairs?