How many different possible tests can be made down a test bank of 8 questions if the test consists of 5 questions?

To solve this problem, we need to calculate the number of different combinations of 5 questions that can be chosen from a test bank of 8 questions. 

This is a combination problem where the order of selection does not matter. The number of combinations of \( r \) items from a set of \( n \) items is given by the combination formula:

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

Here:
- \( n = 8 \) (the total number of questions)
- \( r = 5 \) (the number of questions selected for the test)

Substituting these values into the formula:

\[
C(8, 5) = \frac{8!}{5!(8-5)!} = \frac{8!}{5! \times 3!}
\]

Simplifying this:

\[
C(8, 5) = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = \frac{336}{6} = 56
\]

Thus, there are **56 different possible tests** that can be made.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What if the test consisted of 4 questions instead of 5?
2. How does the combination formula change if repetition of questions was allowed?
3. How many different tests can be made if the order of questions in the test matters?
4. What is the probability of randomly selecting a particular set of 5 questions?
5. How would the calculation change if there were 10 questions in the test bank?

**Tip:** When dealing with combinations, remember that the order of selection does not matter—this differentiates it from permutations.

Discover how many different tests can be created from a pool of 8 questions when selecting 5 questions. Explore the combination formula in detail and learn the calculation steps with an example. Suitable for Grades 10-12.

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