Anil has 8 friends In how many wasys can he invite one or more of his friends to a dinner?

Options

A. `2^(8)`
B. `2^(8)-1`
C. `8^(2)`
D. `.^(8)C_(1)+.^(8)C_(2)+………..+.^(8)C_(6)`

Answer

To solve the problem of how many ways Anil can invite one or more of his 8 friends to dinner, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Choices**: Anil has 8 friends, and for each friend, he has two choices: either to invite them or not to invite them.

2. **Calculating Total Combinations**: Since there are 8 friends and each friend has 2 options (invite or not invite), the total number of ways to invite any combination of friends is given by \(2^n\), where \(n\) is the number of friends. Therefore, the total combinations are:
\[ 2^8 \]

3. **Subtracting the Empty Set**: The calculation \(2^8\) includes the scenario where Anil does not invite any friends at all (the empty set). Since the question specifies that he must invite one or more friends, we need to subtract this one case from our total:
\[ 2^8 - 1 \]

4. **Calculating the Final Answer**: Now, we compute \(2^8\):
\[ 2^8 = 256 \]
Therefore, the number of ways Anil can invite one or more friends is:
\[ 256 - 1 = 255 \]

### Final Answer:
Anil can invite his friends in **255 ways**.