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The question asks to find the number of outcomes using the combination formula:

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

Given:
- \( n = 8 \)
- \( r = 4 \)

The combination formula becomes:

\[
\binom{8}{4} = \frac{8!}{(8 - 4)!4!} = \frac{8!}{4!4!}
\]

Now, let's calculate this.

1. \( 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40,320 \)
2. \( 4! = 4 \times 3 \times 2 \times 1 = 24 \)
3. The formula becomes:

\[
\binom{8}{4} = \frac{40,320}{24 \times 24} = \frac{40,320}{576} = 70
\]

So, the number of outcomes is **70**.

Would you like more details or have any other questions? Here are 5 relative questions to expand the discussion:

1. How does the combination formula differ from the permutation formula?
2. What are some practical examples of using combinations in real life?
3. How would the formula change if the problem used permutations instead?
4. Can you calculate combinations for larger values of \( n \) and \( r \) without a calculator?
5. What is the role of factorial in combination problems?

**Tip:** In combinations, the order of selection does not matter, while in permutations, the order is important.

Use the combination formula below to find the number of outcomes when n = 8 and r = 4.

Learn how to use the combination formula to find the number of outcomes when n = 8 and r = 4. This step-by-step solution explains the combinatorics concept, factorials, and how to compute the result as 70.

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