A man has 10 friends. In how many ways can he | vedclass

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(D) For each of the $10$ friends,the man has $2$ choices: either to invite them or not to invite them.Since there are $10$ friends,the total number of

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$2^{10} - 1$

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(D) For each of the $10$ friends,the man has $2$ choices: either to invite them or not to invite them.Since there are $10$ friends,the total number of ways to invite any number of friends (including zero) is $2 	imes 2 	imes \dots 	imes 2$ ($10$ times),which is $2^{10}$.However,the question specifies that he must invite 'one or more' friends,so we must exclude the case where no friends are invited (i.e.,the case where he chooses not to invite all $10$ friends).Therefore,the required number of ways is $2^{10} - 1$.

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?

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