To answer this question, you'll need to use permutations and factorials.
Factorials are any integer with an ! after it. This means that all of the integers before that number are multiplied together with said number.
This question will use the following formula:
[tex] \frac{n!}{(n-r)!} [/tex]
n represents the amount of items in a set, and r represents the amount of items in each combination within the set.
You have 18 students, and you can choose any combination of 3 students. Plug your values into the formula:
[tex] n = 18, r = 3 [/tex]
[tex] \frac{18!}{(18 - 3)!} = \frac{18!}{15!} = \frac{15! \times 16 \times 17 \times 18}{15!} [/tex]
[tex] \frac{15! \times 16 \times 17 \times 18}{15!} = 16 \times 17 \times 18 = \boxed{4896} [/tex]
There are 4896 different combinations of students that Ms. Lunette can choose.
