Answer:
1820 ways.
Step-by-step explanation:
We have been given that a science teacher needs to choose 12 out of 16 students to serve as peer tutors.
We will use combinations to solve our given problem.
The formula [tex]_{r}^{n}\textrm{C}=\frac{n!}{(n-r)!r!}[/tex] represents number of ways to choose r items from n total items.
Upon substituting our given values in above formula, we will get:
[tex]_{12}^{16}\textrm{C}=\frac{16!}{(16-12)!12!}[/tex]
[tex]_{12}^{16}\textrm{C}=\frac{16!}{4!*12!}[/tex]
[tex]_{12}^{16}\textrm{C}=\frac{16*15*14*13*12!}{4*3*2*1*12!}[/tex]
[tex]_{12}^{16}\textrm{C}=\frac{4*5*7*13}{1}[/tex]
[tex]_{12}^{16}\textrm{C}=1820[/tex]
Therefore, the tutors can be chosen in 1820 different ways.
