Question

How many ways can 6 students sit in a row of 20 chairs

Answer 1

There are 720 ways that everyone can sit.

Answer 2

There are C(20,6) = 38,760 ways to choose 6 of the 20 chairs for students to sit in. Once those chairs are chosen, there are 6! = 720 ways to arrange the 6 students in those 6 chairs. Thus, there are a total of

... 38,760×720 = 27,907,200

ways that 6 students can sit in a row of 20 chairs.

_____

C(n, k) = n!/(k!·(n-k)!)