What is 8!/(6!⋅2!)8! / (6! \cdot 2!)8!/(6!⋅2!)?

The expression is \(\frac{8!}{6! \cdot 2!}\).

We can calculate it step by step:

1. **Factorials**:  
   - \(8! = 8 \times 7 \times 6!\)
   - \(6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720\)
   - \(2! = 2 \times 1 = 2\)

2. Substitute the values into the expression:

   \[
   \frac{8!}{6! \cdot 2!} = \frac{8 \times 7 \times 6!}{6! \cdot 2!}
   \]

3. Cancel out the \(6!\) from the numerator and denominator:

   \[
   = \frac{8 \times 7}{2!} = \frac{8 \times 7}{2}
   \]

4. Simplify the remaining expression:

   \[
   = \frac{56}{2} = 28
   \]

Thus, \(\frac{8!}{6! \cdot 2!} = 28\).

Let me know if you'd like further details or have any questions!

### Related questions:
1. What is the general formula for combinations, and how does it relate to this expression?
2. How do factorials grow with increasing numbers?
3. Can you solve \(\frac{10!}{7! \cdot 3!}\)?
4. What is the meaning of the exclamation mark (!) in mathematics?
5. How do factorials apply in probability theory?

### Tip:
When solving factorial-related problems, always try to cancel out common terms to simplify the expression quickly.

Learn how to calculate 8!/(6!⋅2!) using the factorial formula step-by-step. This problem covers combinatorics concepts such as the binomial coefficient and factorials, suitable for Grades 9-12.

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