Evaluate the permutation 5P2 (i.e., the number of ordered ways to choose 2 distinct items from 5 distinct items).

Introduction / Context:nP r counts ordered selections of r distinct items from n distinct items. Here, n = 5 and r = 2.

Given Data / Assumptions:

• n = 5, r = 2.
• Formula: nP r = n! / (n − r)! = n * (n − 1) * … * (n − r + 1).

Concept / Approach:Compute directly using the short product: 5 * 4.

Step-by-Step Solution:

Verification / Alternative check:Factorial form: 5! / 3! = (120) / 6 = 20, consistent.

Why Other Options Are Wrong:15 would be 5C2 (unordered); 18 and 122 are unrelated.

Common Pitfalls:Confusing permutations (ordered) with combinations (unordered).

Final Answer:20