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.
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
To determine the number of ways 10 runners can finish a race, you need to calculate the factorial of 10, denoted as 10!.
To calculate a factorial, you multiply a number by all of its preceding positive integers until you reach 1. So, 10! is calculated as follows:
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
Therefore, there are 3,628,800 different ways that 10 runners can finish the race.