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The problem asks to calculate the number of combinations of 8 things taken 6 at a time, using the formula for combinations:

\[
C_r = \frac{n!}{r!(n-r)!}
\]

### Substituting the given values:
- \( n = 8 \)
- \( r = 6 \)

\[
C_6 = \frac{8!}{6!(8-6)!} = \frac{8!}{6! \cdot 2!}
\]

#### Calculating step by step:

1. **Factorials**:
   \[
   8! = 8 \times 7 \times 6!
   \]
   So:
   \[
   \frac{8!}{6!} = 8 \times 7 = 56
   \]

2. **Divide by \( 2! \)**:
   \[
   2! = 2 \times 1 = 2
   \]
   \[
   \frac{56}{2} = 28
   \]

### Final Answer:
The number of combinations is:

\[
\boxed{28}
\]

Would you like a more detailed explanation or help with a related topic?  

Here are 5 questions to expand your understanding:
1. How does the formula for combinations differ from permutations?
2. What is the significance of factorials in counting problems?
3. What would the result be for \( C_8 \) (all 8 items chosen)?
4. How is \( C_6 \) related to \( C_2 \) when \( n = 8 \)?
5. Can combinations apply to non-integer or fractional values?

**Tip:** Always verify calculations step by step to ensure accuracy in factorial-based problems!

Find the number of combinations of 8 things taken 6 at a time.

Learn how to calculate the number of combinations of 8 items taken 6 at a time. This detailed solution demonstrates the use of the combination formula C_r = n! / (r!(n-r)!) and explains factorial-based calculations step by step. Perfect for high school students in Grades 9-12.

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