Question

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

• A. $128$
• B. $256$
• C. $127$
• D. $130$

Answer 1

The correct option is C

$127$

Finding the number of ways in which a man can invite one or more of them for a tea party:

Given, the total number of friends $=7$

Since there are two options for each friend, either invite or do not invite them,

Total number of ways of inviting seven friends $=2^7$

Now, in combinations theory, for $0$ friends, we have $2$ options,

$=2^0$

$=1$

In order to calculate the number of ways of inviting or not inviting seven friends, we need to exclude $2^0$ number of ways,

$=2^7-1$

$=128-1$

$=127$

$\therefore$the man can choose to invite or not invite seven friends in $\mathbf{127}$ number of ways.

Hence, Option (C) is correct.