Q

QuestionMathematics

If the order is important, then you would use a permutation. If the order is not important, then a combination is appropriate. ** 2.** An example where these ideas might be applicable is when forming a committee from a group of people. Suppose we have 10 candidates, and we want to form a committee of 3 members. Here, the order in which the members are chosen does not matter, so we would use a combination. ** 3.** In the example above, we know to use a combination because the order of selecting the committee members is not relevant. If the problem involved arranging the candidates in a particular order (e.g., seat them in a row), then we would use a permutation instead. ** 4.** Let's look at an example using both combinations and permutations. Example: In a group of 10 people, determine the number of ways to: a) Form a committee of 3 members (using combinations) b) Arrange the 10 people in a line (using permutations) **Step 1:** a) To calculate the number of ways to form a committee of 3 members from 10 people, we use the combination formula: **Step 2:** a) Plugging in our values, we get: So, there are 120 different ways to form a committee of 3 members from a group of 10 people. **Step 3:** b) To calculate the number of ways to arrange 10 people in a line, we use the permutation formula: **Step 4:** b) Plugging in our values, we get: So, there are 3,628,800 different ways to arrange 10 people in a line. **