How many ways can 6 students sit in a row of 21 chairs for a photograph?

Question

39070080? 39069525? 39069428?

Answer 1

Ok so we have 21 chairs and 6 students, and need to determine the # of ways those students can be arranged in the chairs.

This will be solved using either the permutations or combinations formula.

The 6 students are different people, so simply swapping two students would be a different "way" to arrange them. This means that order matters. Therefore, it is a permutations problem, not combinations.

The formula for permutations directly gives the answer (# of ways the students can be arranged in the chairs), and we just need to use n=21 and r=6.

Use a calculator for permutations: "P(21,6)" or "21 nPr 6" which will give the answer 39070080.

Hope this helps. :)

Answer 2

Ways differ from each other only by order so this is permutations from 21 by 6: P(21,6) = 39070080