Question

How many combinations of 4 students can a teacher choose from 30 students?

A.
657,720

B.
120

C.
810,000

D.
27,405

Answer 1

you are being asked for "30 choose 4" written as
\[\binom{30}{4}\] or sometimes \[_{30}C_4\] or even
\[_{30}C_4\] and computed via
\[\binom{30}{4}=\frac{\overbrace{30\times 29\times 28\times 27}^{\text {4 terms}}}{4\times 3\times 2}\]

Answer 2

most calculators have this button so you don't have to do the actual computation, but if you have to do it by hand, since the answer is a whole number, cancel first, multiply last
i would do this
http://www.wolframalpha.com/input/?i=30+choose+4