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A man is offered to toss a coin a certain number n times and if it heads exactly 5 times, he will receive a prize.

A man is offered to toss a coin a certain number "n" times and if it heads

exactly 5 times, he will receive a prize. At first, he must decide for himself how many times he will throw the

piece of money. What number should he choose in order to maximize his chances of winning and what then is the

probability that he wins ?

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