Question

In a race between 18 people, how many ways can the top 5 finishers be arranged?

Answer 1

The answer is 8568 ways.

Explanation:

In order to determine the amount of ways that top 5 finishers can be arranged, we need to understand "Combinations"

Combination is the same that how lotteries work. The numbers are drawn one at a time, and if we have the lucky numbers (no matter what order) we win.

The best way to explain it is to:

1. assume that the order does matter.
2. then alter it so the order does not matter.

In this case, this combination is without repetition.

I have attached an image that shows the notation and formula of the combination is without repetition.

So,

n=18

r=5

Applying the formula:

`(18!)/(5!*(18-5)!) \\(18!)/(5!*(13)!) \\(18*17*16*15*14)/(5*4*3*2) \\8568`

Finally, the answer is 8568 ways.

Answer 2

This would use the combination formula, since the order of the people doesn't matter, other than having 5 top finishers.

C(18,5) = 18! / (5!(18-5)!) = 8,568 ways