A man has 7 friends. In how many ways can he | vedclass

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(C) For each of the $7$ friends,the man has $2$ choices: either to invite them or not to invite them.Since there are $7$ friends,the total number of w

Vedclass · Accepted Answer

$127$

Vedclass · Answer

(C) For each of the $7$ friends,the man has $2$ choices: either to invite them or not to invite them.Since there are $7$ friends,the total number of ways to invite any number of friends (including the case where no one is invited) is $2^7 = 128$.However,the question specifies that he must invite 'one or more' friends,which means we must exclude the case where no friend is invited.The number of ways to invite no friends is $^7C_0 = 1$.Therefore,the required number of ways is $2^7 - 1 = 128 - 1 = 127$.

$A$ man has $7$ friends. In how many ways can he invite one or more of them for a tea party?

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