Rearranging Student Council Positions?

📌 CONCEPT: To find the number of ways to arrange the student council positions, we need to calculate the number of permutations of the representatives and then consider the selection of event coordinators from the remaining students.

📐 RULE / FORMULA: The total number of ways to arrange the positions is given by the formula P(12, 4) * C(8, 2), where P(n, r) represents the permutation of n items taken r at a time and C(n, r) represents the combination of n items taken r at a time.

💡 WORKED EXAMPLE: Let's calculate the number of ways to arrange the positions. First, we find the permutation of 12 students taken 4 at a time: P(12, 4) = 12! / (12-4)! = 11,880. Then, we find the combination of 8 remaining students taken 2 at a time: C(8, 2) = 8! / (2!(8-2)!) = 28. Multiplying these values, we get 11,880 * 28 = 332,640 different ways to arrange the positions.

⚠️ COMMON MISTAKE: Students often forget to consider the decreasing number of choices for the event coordinators, which affects the total number of permutations. It's essential to choose the representatives first and then select the event coordinators from the remaining pool of students.