how many ways can 10 runners finish a race. 10 could finish 10 9 could finish 9 and so on would I times 10*9*8 ect that number seems way to big.

Answer 1

actually it is much bigger than that

1st place --- 10 different runners
2nd place ---9
3rd place ---8
...
last place --- 1 runner

number of ways = 10*9*8*7*...*2*1
= 3,628,800

What your 10*9*8 is
is the ways 1st, 2nd and third place could happen