A man has 7 friends. In how many ways can be invite one or more of them to a party ?

Answer

To solve the problem of how many ways a man can invite one or more of his 7 friends to a party, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have 7 friends, and we want to find out how many different combinations of these friends can be invited to a party, with the condition that at least one friend must be invited.

2. **Total Combinations**: For each friend, there are two choices: either to invite them or not to invite them. Therefore, for 7 friends, the total number of combinations (including the case where no friends are invited) is given by \(2^n\), where \(n\) is the number of friends.

\[ \text{Total combinations} = 2^7 = 128 \]

3. **Excluding the Empty Set**: Since we need to invite at least one friend, we must exclude the case where no friends are invited. The only combination that represents this scenario is the empty set.

\[ \text{Combinations with at least one friend} = 128 - 1 = 127 \]

4. **Final Answer**: Therefore, the total number of ways to invite one or more friends to the party is:

\[ \boxed{127} \]