Question

Ms. Chang has 16 students in her class. She wants to send 3 of her students to pick up books for the class.

How many combinations of students can she choose?

Answer 1

you are being asked for \(\dbinom{16}{3}\) read "sixteen choose 3" and computed via
\[\dbinom{16}{3}=\frac{16\times 15\times 14}{3\times 2}\]

Answer 2

16C3 = 560

Answer 3

This is a lesson related to "Permuatations and Combinations". When order is not necessary, you use "C" for combinations; when order IS necessary, you use "P" for permutations.
Why do we use "C" in this case, because order is not important. I mean let's say you have got three students called Amy, Brian, and Ahmed, isn't it the same when I say "Ahmed, Amy, and Brian"? Yes, it is because they are the same people at the end of the day!
Hence, 16 C 3 = 560, where
the number BEFORE C is the TOTAL number of available students and the number AFTER C is the number of the desired outcome = 3 students. Okay?