Question

The freshman class has 160 students. Each freshman must write three reports from a list of 12 novels that the teacher has assigned them to read. How many different combinations of novels can a freshman student choose to write reports on?

Answer 1

you are being asked for
\[\binom{12}{3}\] sometimes written as
\[_{12}C_3\] or even
\[^{12}C_3\] and computed via
\[\binom{12}{3}=\frac{\overbrace{12\times 11\times 10}^{\text{ 3 terms}}}{3\times 2}\]

Answer 2

cancel first, multiply last, since the answer is obviously a whole number