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

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
confused
Posts: 20
Joined: Sun Feb 22, 2009 10:07 pm

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

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
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
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
Posts: 20
Joined: Sun Feb 22, 2009 10:07 pm

### Re: find number of ways seven runners can finish race

So b is 7P3 and c is 7C3?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
So b is 7P3 and c is 7C3?
I do believe you've got it!