Question

15 runners are competing in a race. if the top 3 runners are going to the olympics, how many different groups of 3 could be chosen for the olympics?

Answer 1

you are being asked to compute the number of ways to choose 3 out of 15, written as
\[\dbinom{15}{3}\] read "fifteen choose 3" and computed via
\[\dbinom{15}{3}=\frac{15\times 14\times 13}{3\times 2}\]
divide first, multiply last

Answer 2

is that a combination? :)

Answer 3

If order matters (ie if there's a first, second and third place), then you use a permutation

If order doesn't matter (as long as you place in the top 3, who cares), then use a combination

Answer 4

My guess is that there is no first, second or third distinctions for qualifying for the olympics, so order doesn't matter

Answer 5

thank you both ! :D

Answer 6

sure thing