Question

some students in a gym class are wearing blue jerseys, and the rest are wearing red jerseys. there are exactly ways to pick a team of three players that includes at least one player wearing each color. compute the number of students in the class.

Answer 1

To calculate the number of students in the class, use the given information about the number of ways to pick a team of three players that includes at least one player wearing each color.

Step-by-step explanation:

To calculate the number of students in the class, let's assume the number of students wearing blue jerseys is x and the number of students wearing red jerseys is y. We are given that there are exactly ways to pick a team of three players that includes at least one player wearing each color.

The total number of ways to choose a team of three players from a group of x students is C(x,3) = x(x-1)(x-2)/3!, where C(x,3) represents the number of combinations of x objects taken 3 at a time.

The total number of ways to choose a team of three players from a group of y students is C(y,3) = y(y-1)(y-2)/3!.

Since there are ways to pick a team of three players that includes at least one player wearing each color, we have the equation x(x-1)(x-2)/3! × y(y-1)(y-2)/3! = .

Simplifying this equation will give us the value of x+y, which represents the total number of students in the class.