To determine the number of different 4-person committees that can be made out of 15 students, let's use the Combination Formula.
where n = the total number of choices and r = the total number of selections.
In the question, our n = 15 because there are 15 students to choose from. Our r = 4 because 4 selections will be made from 15 students.
Let's replace the variables in the formula with their corresponding numerical value.
Then, solve. Here are the steps.
1. In the denominator, subtract 15 and 4 first.
2. Expand 15! until 12 only and cancel 11! Expand 4! too.
3. Multiply the numbers in the numerator and denominator.
4. Divide the numerator by the denominator.
Therefore, there are 1, 365 different ways of forming a 4-person committee out of 15 students.