Question

How many ways can 3 students sit in a row of 20 chairs for a photograph?

Answer 1

Since we want to create groups of 3 students among 20 possible spots, and the order of the elements (students) inside each group of 3 is important (the order of students change the group and the photograph), we have a permutation problem.

The formula to calculate a permutation of n choose p is:

`P(n,p)=(n!)/((n-p)!)`

For this problem, let's use n = 20 and p = 3, so we have:

`\begin{gathered} P(20,3)=(20!)/((20-3)!) \\ P(20,3)=(20!)/(17!) \\ P(20,3)=(20\cdot19\cdot18\cdot17!)/(17!) \\ P(20,3)=20\cdot19\cdot18 \\ P(20,3)=6840 \end{gathered}`

So there are 6840 different ways the 3 students can sit in the chairs.