Given:
The number of runners = 600 runners.
The number of places = 3 ( first three).
Required:
We need to find a number of different ways to arrange a first, second, and third place.
Explanation:
[tex]\text{ Out of 600 runners,3 can be picked }600C_3\text{ ways.}[/tex]
These three can be arranged first, second and third place in 3! ways.
[tex]The\text{ number of arrangements = }600C_3\times3![/tex]
[tex]The\text{ number of arrangements = }\frac{600!}{3!(600-3)!}\times3![/tex]
[tex]The\text{ number of arrangements = }\frac{600!}{3!(597)!}\times3![/tex]
[tex]The\text{ number of arrangements = }\frac{600\times599\times598\times597!}{(597)!}[/tex]
[tex]The\text{ number of arrangements = }600\times599\times598[/tex]
[tex]The\text{ number of arrangements = 214,921,200 ways}[/tex]
Final answer:
[tex]The\text{ number of arrangements = 214,921,200 ways}[/tex]
