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# A player in a certain game has a deck of 40 cards. There are

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A player in a certain game has a deck of 40 cards. There are [#permalink]  21 Mar 2004, 09:22
A player in a certain game has a deck of 40 cards. There are 5 distinct cards within the deck, and if he holds all 5 cards in his hand in any order he wins the game. If he draws 6 cards into his hand to begin the game, then 1 card for each subsequent turn, then what is probability that he wins the game after 20 turns?
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After 20 turns, then total number of cards in hand is: 40C(6+20) = 40C26
# of possible ways of drawing the 5 distinct cards out of 40: 40C5
Possibility of drawing the 5 distinct cards out of 26 drawn:
40C5 / 40C26
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P = 26C5/40C5

I assume that the player does not reutrn the unwanted card back to the deck.
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