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:
[tex]C_{(r,n)}=\frac{n!}{r!(n-r)!}[/tex]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
[tex]\begin{gathered} C_{}(3,16)=\frac{16!}{3!(16-3)!} \\ C(3,16)=560 \end{gathered}[/tex]The principal can pick up to 560 different groups of Ms Guzman's class.
