Ralph, Mario, Jack, Laura, and Maria are in the math club. The club advisor will assign students to 3-person teams at the next math team competition. How many different 3-person teams can be formed from these five students?
would this be 10, because of 5 * 4 * 3 / 3 * 2 * 1?
yes
Yes, you are correct! To solve this problem, we can use the formula for combinations, which is calculated by dividing the factorial of the total number of students by the factorial of the number of students in each team and the factorial of the remaining students.
In this case, we have 5 students and are forming 3-person teams. So, we can calculate it as:
5! / (3! * (5-3)!)
Where "!" denotes factorial.
Simplifying the equation:
5! = 5 * 4 * 3 * 2 * 1
3! = 3 * 2 * 1
(5-3)! = 2! = 2 * 1
Plugging in the values:
5! / (3! * (5-3)!) = (5 * 4 * 3 * 2 * 1) / ( (3 * 2 * 1) * (2 * 1) )
= (5 * 4) / (2 * 1)
= 20 / 2
= 10
So, there are 10 different 3-person teams that can be formed from these five students.