Specify the number of ways to perform the task described. Give your answers using $P(n, r)$ or $C(n, r)$ notation.
On a biology quiz, a student must match three terms with their definitions. Assume that the same term cannot be used twice.
Answer
Final Answer: There are \(\boxed{6}\) ways to match the terms with their definitions.
Step 1 ：The student has three terms and three definitions. The task is to match each term with its correct definition. This is a permutation problem because the order in which the terms are matched to the definitions matters.
Step 2 ：The formula for permutations is \(P(n, r) = \frac{n!}{(n-r)!}\), where \(n\) is the total number of items, and \(r\) is the number of items to choose. In this case, \(n = r = 3\) because there are three terms and the student must match all three.
Step 3 ：Using the formula, we find that there are \(P(3, 3) = 6\) ways to match the terms with their definitions.
Step 4 ：Final Answer: There are \(\boxed{6}\) ways to match the terms with their definitions.
