how many ways can 8 athletes finish a 200 meter sprint?

Answer

Explanation:

Step1: Identify the problem type

This is a permutation problem. The number of ways to arrange (n) distinct objects is (n!). Here (n = 8) (the number of athletes).

Step2: Calculate the factorial

The formula for (n!) is (n\times(n - 1)\times\cdots\times1). So (8! = 8\times7\times6\times5\times4\times3\times2\times1). [ \begin{align*} 8\times7&=56\ 56\times6&=336\ 336\times5& = 1680\ 1680\times4&=6720\ 6720\times3&=20160\ 20160\times2&=40320\ 40320\times1&=40320 \end{align*} ]

Answer:

40320