Find the number of ways in which a man can invite one or more of his 8 friends to a dinner?

Answer

To solve the problem of finding the number of ways a man can invite one or more of his 8 friends to dinner, we can follow these steps:

### Step 1: Understand the problem
The man can invite any combination of his 8 friends, but he must invite at least one friend.

### Step 2: Calculate total combinations
For each friend, there are two choices: either to invite the friend or not to invite the friend. Therefore, for 8 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.

\[ \text{Total combinations} = 2^8 \]

### Step 3: Exclude the case of inviting no friends
Since we need to find the number of ways to invite one or more friends, we must exclude the case where no friends are invited.

\[ \text{Combinations with at least one friend} = 2^8 - 1 \]

### Step 4: Calculate the final result
Now, we can calculate \(2^8\):

\[ 2^8 = 256 \]

Subtracting the one case where no friends are invited:

\[ 256 - 1 = 255 \]

### Conclusion
Thus, the number of ways in which the man can invite one or more of his 8 friends to dinner is **255**.

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