Question

There are 15 students in a social studies class. Two students will be selected to present their term projects today. On how many different orders can two students be selected?

Answer 1

Since the order matters, this is a permutation rather than a combination.
\[\small15\large P\small2\large=\frac{15!}{(15-2)!} \]

Answer 2

How do I do this? I'm not very familiar with this...

Answer 3

The factorial "\(!\)" is used in the following way:
\(5!=5\times4\times3\times2\times1\)

\(7!=7\times6\times5\times4\times3\times2\times1\)

\((15-2)!=13!=13\times12\times11\times\ldots\times3\times2\times1\)

Answer 4

\[ \frac{15!}{(15-2)!}=\frac{15!}{13!}=\frac{15\times14\times13\times12\times\dots\times3\times2\times1}{13\times12\times\dots\times3\times2\times1}=\frac{15\times14\cancel{\times13!}}{\cancel{13!}}\]