Math Problem Statement
How many different possible tests can be made down a test bank of 8 questions if the test consists of 5 questions?
Solution
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 items from a set of items is given by the combination formula:
Here:
- (the total number of questions)
- (the number of questions selected for the test)
Substituting these values into the formula:
Simplifying this:
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:
- What if the test consisted of 4 questions instead of 5?
- How does the combination formula change if repetition of questions was allowed?
- How many different tests can be made if the order of questions in the test matters?
- What is the probability of randomly selecting a particular set of 5 questions?
- 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.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Combinations
Formulas
Combination formula
Theorems
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Suitable Grade Level
Grades 10-12
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