[MOVED] find number of ways seven runners can finish race

[confused]

There are seven runners in a race. They all finish the race, and no two runners finish the race at the same time. Find:

a: the number of ways that the runners can finish the race.
b: the number of ways, in order, that the first three runners could finish the race.
c: the number of ways, regardless of order, that the first three runners could finish the race.

For a, I think its just 7!. But I don't understand what is the difference between b and c.

[stapel_eliz]

For a, I think its just 7!. But I don't understand what is the difference between b and c.

I agree with you on the answer to part (a).

With respect to parts (b) and (c), the difference, as I understand it, is between choosing the first three runners in order ("A places first, B places second, and C places third" being distinct from "B places first, A places second, and C places third") and, on the other hand, just naming the top three finishers (where "A, B, and C" is the same as "B, A, and C"). So the difference is between choosing three in order (that is, using permutation) and without order (that is, using combinations).

Does that help?

[confused]

So b is 7P3 and c is 7C3?

[stapel_eliz]

So b is 7P3 and c is 7C3?

I do believe you've got it!