Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityMedium
A manager is arranging 6 different tasks for an employee to complete. In how many different orders can the employee complete all 6 tasks?
- A36
- B46,656
- C720
- D6
Show answer & explanationAnswer & explanation
Correct answer: C. 720
This is a permutation problem because the order of the tasks matters. Since all 6 tasks are being arranged, it's a permutation of all items, which is n!. So, 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720.
Why the other options are wrong
- A. This is 6^2, not 6!.
- B. This is 6^6, incorrect.
- D. This is just n, not n!.
Permutations
A permutation is an arrangement of items from a set where the order of arrangement matters.
- Formula: P(n, k) = n! / (n-k)!, where n is total items and k is items to arrange.
- If all items are arranged (k=n), the formula simplifies to n!.
- Used when determining sequences, rankings, or ordered selections.
Memory trick: Permutation: 'Position' always counts.