Topic
Class 10A has 30 students. The homeroom teacher wants to choose a class committee consisting of 3 members: 1 class president, 1 academic assistant class, and 1 literary assistant class. Ask the teacher how many ways to choose a class committee?
Solution method – See details
We select each student in successive steps
Step 1: Calculate the number of ways to choose 1 class president out of 30 students
Step 2: Calculate the number of ways to choose 1 student to be the assistant class member out of 29 students (except for the class president selected in step 1)
Step 3: Calculate the number of ways to choose 1 student to be the assistant class in the remaining 28 students (except for the 2 students selected in the 2 steps above).
Step 4: Apply the multiplication rule to calculate the total number of ways to choose
Detailed explanation
Choosing a class staff consisting of 1 class president, 1 academic assistant class and 1 literary assistant class is to perform three consecutive actions: choose a class president, then choose an academic vice class, and finally choose 1 Literature class.
Since class 10A has a total of 30 students, there are 30 ways to choose a class president.
Since the teacher has chosen a student to be the class president, we now have 29 ways to choose a class vice president.
Since the teacher has chosen one student to be the class president and one to be the vice-president, we now have 28 ways to choose an assistant class.
So the teacher has a total of 30.29.28 = 24 360 ways to choose a class committee.
