In how many ways can 5 people be seated in a row of 8 seats?

I solved this with the similar method to “how many ways can you arrange the letters of mississippi”, which appears in the video in the two month plan. If we assume each person is unique, then each “person in seat” occurs once, and the “seat with no person” occurs three times. Another way to ask this question could be “how many ways can you arrange the letters ABCDEXXX”, where A,B,C,D,E represent each of 5 people, and X represents a seat with no person.

Factorial of total # of spaces / Product of Factorials of occurrences of each option

= 8! / (1! x 1! x 1! x 1! x 1! x 3!)

= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / 3 x 2 x 1

= 8 x 7 x 6 x 5 x 4

= 6,720