Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityHard
A librarian is organizing new books on a shelf. There are 7 new novels and 5 new non-fiction books. If the librarian wants to choose 3 novels and 2 non-fiction books to display on a special stand, how many different combinations of books can be chosen?
- A35
- B720
- C120
- D350
Show answer & explanationAnswer & explanation
Correct answer: D. 350
This problem involves combinations for two separate selections. For novels: C(7, 3) = 7! / (3! * (7-3)!) = 7! / (3! * 4!) = (7*6*5) / (3*2*1) = 35. For non-fiction: C(5, 2) = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5*4) / (2*1) = 10. To find the total number of combinations, multiply the results: 35 * 10 = 350.
Why the other options are wrong
- A. This is only the number of ways to choose 3 novels.
- B. This is incorrect; it might be a permutation of more items or a product of incorrect combinations.
- C. This is incorrect; it might be a permutation of 5 items or a product of incorrect combinations.
Combinations (Multiple Groups)
The number of ways to choose items from multiple distinct groups where the order of selection within each group does not matter.
- Use the combination formula C(n, k) for each group.
- Multiply the results of each group's combination calculation.
- Order of selection does not matter.
Memory trick: Separate groups, combine choices with multiplication.