Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityMedium
A student is randomly selecting 3 books from a shelf containing 8 different books. How many different combinations of 3 books can the student select?
- A336
- B6
- C56
- D24
Show answer & explanationAnswer & explanation
Correct answer: C. 56
This is a combination problem because the order of selecting the books does not matter. The formula for combinations is C(n, k) = n! / (k! * (n-k)!), where n is the total number of items and k is the number of items to choose. C(8, 3) = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8 * 7 * 6 * 5!) / ((3 * 2 * 1) * 5!) = (8 * 7 * 6) / 6 = 56.
Why the other options are wrong
- A. This would be a permutation P(8, 3) = 8 * 7 * 6 = 336, where order matters.
- B. Incorrect, perhaps a simple arithmetic error.
- D. Incorrect, this would be 8 * 3.
Combinations
A combination is a selection of items from a set where the order of selection does not matter.
- Formula: C(n, k) = n! / (k! * (n-k)!).
- Used when forming groups, committees, or selecting items where arrangement is irrelevant.
- Always results in a smaller number than permutations for the same n and k (if k > 1).
Memory trick: Combination: 'Choose' (order doesn't matter). Permutation: 'Position' (order matters).