Question

The principal randomly picks 3 students from Ms. Guzman's class which has 16 students in it. How many different groups of 3 does the principal have to pick from?

Answer 1

To calculate how many groups of 6 he can pick out of 16 students you have to calculate a combination. To do so you have to apply the following formula:

`C_((r,n))=(n!)/(r!(n-r)!)`

Where

n represents the total number of students in the class

r represents the number of students he wants to pick up

So for this exercise you have to use n=16 and r=3

`\begin{gathered} C_{}(3,16)=(16!)/(3!(16-3)!) \\ C(3,16)=560 \end{gathered}`

The principal can pick up to 560 different groups of Ms Guzman's class.