Question

How many ways can 10 students be seated in a room with 13 chairs?

Answer 1

Use combination to solve it
13C10 = $\dfrac{13!}{10! \times (13-10)!}$
13C10 = $\dfrac{13 \times 12 \times 11 \times 10!}{10! \times 3!}$
13C10 = $\dfrac{13 \times 12 \times 11}{3!}$
13C10 = $\dfrac{13 \times 12 \times 11}{3 \times 2 \times 1}$
13C10 = $\dfrac{1716}{6}$
13C10 = 286
There are 286 ways