How many unordered sets are there of four items chosen from eight?
 sets

To determine the number of unordered sets of four items chosen from a total of eight, we use the concept of combinations. For an unordered set (where the order of selection doesn't matter), the formula for combinations is:

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

where:
- \( n = 8 \) (the total number of items),
- \( r = 4 \) (the number of items to choose).

Plugging in the values:

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

Now, calculate each part:
1. \( 8! = 8 \times 7 \times 6 \times 5 \times 4! \), but since it divides by \( 4! \), we can simplify this to \( 8 \times 7 \times 6 \times 5 \).
2. Calculating the above:

   \[
   8 \times 7 = 56
   \]
   \[
   56 \times 6 = 336
   \]
   \[
   336 \times 5 = 1680
   \]

3. Now divide by \( 4! = 24 \):

   \[
   \frac{1680}{24} = 70
   \]

So, there are **70 unordered sets** of four items chosen from eight.

Would you like further details or have any questions?

### Related Questions
1. How would the answer change if we chose 5 items from 8 instead of 4?
2. What if we chose ordered sets instead of unordered sets?
3. How many unordered sets are there of three items chosen from eight?
4. What is the total number of combinations if we choose two items from eight?
5. How does this calculation change for a scenario with replacement?

### Tip:
When solving combination problems, always simplify factorial expressions as much as possible before multiplying to make calculations easier.

How many unordered sets are there of four items chosen from eight?

Learn how to calculate the number of unordered sets of four items chosen from a total of eight using combinations. This problem involves combinatorics principles and combination formulas, making it ideal for students in Grades 10-12.

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