In how many ways can a person invites his 2 or more than 2 friends out of 5 friends for dinner?

Answer

To solve the problem of how many ways a person can invite 2 or more friends out of 5 friends for dinner, we can follow these steps:

### Step 1: Identify the total number of friends
The total number of friends available is 5.

### Step 2: Determine the combinations needed
We need to find the number of ways to invite 2, 3, 4, or all 5 friends. This means we will calculate the combinations for each of these cases.

### Step 3: Use the combination formula
The combination formula is given by:
\[ nCr = \frac{n!}{r!(n-r)!} \]
where \( n \) is the total number of items to choose from, \( r \) is the number of items to choose, and \( ! \) denotes factorial.

### Step 4: Calculate the combinations for each case
1. **Inviting 2 friends**:
\[ \text{Number of ways} = 5C2 = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10 \]

2. **Inviting 3 friends**:
\[ \text{Number of ways} = 5C3 = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10 \]

3. **Inviting 4 friends**:
\[ \text{Number of ways} = 5C4 = \frac{5!}{4!(5-4)!} = 5 \]

4. **Inviting all 5 friends**:
\[ \text{Number of ways} = 5C5 = \frac{5!}{5!(5-5)!} = 1 \]

### Step 5: Sum the combinations
Now, we add all the combinations calculated:
\[ 10 \text{ (for 2 friends)} + 10 \text{ (for 3 friends)} + 5 \text{ (for 4 friends)} + 1 \text{ (for 5 friends)} = 26 \]

### Final Answer
Thus, the total number of ways a person can invite 2 or more friends out of 5 friends for dinner is **26**.

---