How many different products can be obtained by multiplying two or more of the numbers 2, 5, 6, 7, 9 (without repitition)?

Answer

To find how many different products can be obtained by multiplying two or more of the numbers 2, 5, 6, 7, and 9 (without repetition), we can follow these steps:

### Step 1: Identify the numbers
We have the numbers: 2, 5, 6, 7, and 9. There are a total of 5 numbers.

### Step 2: Determine combinations for multiplication
We need to find the number of ways to choose 2 or more numbers from these 5 numbers. We will calculate the combinations for choosing 2, 3, 4, and all 5 numbers.

### Step 3: Calculate combinations
Using the combination formula \( nCr = \frac{n!}{r!(n-r)!} \):

1. **Choosing 2 numbers**:
\[ 5C2 = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10 \]

2. **Choosing 3 numbers**:
\[ 5C3 = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10 \]

3. **Choosing 4 numbers**:
\[ 5C4 = \frac{5!}{4!(5-4)!} = 5 \]

4. **Choosing all 5 numbers**:
\[ 5C5 = \frac{5!}{5!(5-5)!} = 1 \]

### Step 4: Sum the combinations
Now, we add all the combinations calculated:
\[ 5C2 + 5C3 + 5C4 + 5C5 = 10 + 10 + 5 + 1 = 26 \]

### Conclusion
Thus, the total number of different products that can be obtained by multiplying two or more of the numbers 2, 5, 6, 7, and 9 is **26**.

---