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, you are correct! The number of different 3-person teams that can be formed from five students (Ralph, Mario, Jack, Laura, and Maria) can be calculated using the formula for combinations.

You can use the combination formula or shorthand notation, which is often denoted as "nCk," where n represents the number of students to choose from, and k represents the number of students to be chosen.

The formula for combinations is given by:

nCk = n! / (k! * (n-k)!)

In this case, we need to choose 3 students from a group of 5. So, it would be written as:

5C3 = 5! / (3! * (5-3)!)

Now let's calculate it step by step:

5! = 5 * 4 * 3 * 2 * 1 = 120
3! = 3 * 2 * 1 = 6
(5-3)! = 2! = 2 * 1 = 2

Substituting these values back into the equation:

5C3 = 120 / (6 * 2) = 120 / 12 = 10

Therefore, there are 10 different 3-person teams that can be formed from these five students.

Yes, that is correct. To calculate the number of different 3-person teams that can be formed from 5 students, you can use the formula for combinations:

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

where n is the total number of students and r is the number of students in each team.

In this case, n = 5 and r = 3. Plugging these values into the formula:

C(5, 3) = 5! / (3!(5-3)!)
= 5! / (3!2!)
= (5 * 4 * 3!) / (3! * 2 * 1)
= (5 * 4 * 3) / (3 * 2 * 1)
= 60 / 6
= 10

So, there are 10 different 3-person teams that can be formed from these five students.