Nancy and Karen play a game of cards as follows. Nancy draws 3 cards out of a regular deck of 52 cards without replacement: if she draws at least one ace, she wins. Otherwise, Karen wins. Suppose they play the games 10 times, and after each time, the cards are placed back in the deck and reshuffled. (a) Find the probability that Nancy wins exactly 4 times. (b) Find the expected number of times Karen wins.

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Nancy and Karen play a game of cards as follows. Nancy draws 3 cards out of a regular deck of 52 cards without replacement: if she draws at least one ace, she wins. Otherwise, Karen wins. Suppose they play the games 10 times, and after each time, the cards are placed back in the deck and reshuffled.

(a) Find the probability that Nancy wins exactly 4 times.

(b) Find the expected number of times Karen wins.

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