Question

6) Johnny Awesome decided to run a marathon while on vacation. There are 600 runners. How many differentways can first, second, and third place be arranged?600

Answer 1

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.

Step-by-step explanation:

`\text{ Out of 600 runners,3 can be picked }600C_3\text{ ways.}`

These three can be arranged first, second and third place in 3! ways.

`The\text{ number of arrangements = }600C_3*3!`

`The\text{ number of arrangements = }(600!)/(3!(600-3)!)*3!`

`The\text{ number of arrangements = }(600!)/(3!(597)!)*3!`

`The\text{ number of arrangements = }(600*599*598*597!)/((597)!)`

`The\text{ number of arrangements = }600*599*598`

`The\text{ number of arrangements = 214,921,200 ways}`

Final answer:

`The\text{ number of arrangements = 214,921,200 ways}`