Question

A teacher randomly selects three students each month from a class of 30 students to be the students of the month. Each student receives a

special certificate special seating in class, and a free homework pass. How many different groups of three students could be selected?
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Answer 1

Using the combination formula, there are 4060 different groups of three students that could be selected from a class of 30 students.

Step-by-step explanation:

The student's question is about how many different groups of three students the teacher can select from a class of 30 students for the student of the month award. This is a combination problem because the order in which the students are selected does not matter.

To calculate the number of different groups possible, we use the combination formula, which is given by:

C(n, k) = n! / (k!(n-k)!)

Where:

• n is the total number of students
• k is the number of students to select
• ! denotes factorial, the product of all positive integers up to that number

Substituting the given values:

C(30, 3) = 30! / (3!(30-3)!) = (30x29x28) / (3x2x1) = 4060

Therefore, there are 4060 different groups of three students that could be selected.