In how many ways can six people sit in six seats in a line at a cinema? In how many ways can the six people sit around a dinner table eating pizza after the movie?

Step-by-step explanation:

the answer is the same.

sitting in a ring at a table is the same as cutting that ring open, stretch it out and have a line of seats.

so, it is 6!

as we have a set of 6 people, and for every attempt we pick all 6 people, and the order matters.

formally it is therefore the permutation

P(6, 6) = 6! / (6-6)! = 6! = 720