# What is the probability of ending in battle royale Top 5?

In a battle royale, there are 100 players. I'm one of those players. For the exercise, we suppose that each player have same game skills.

What is my chance of ending in the Top 5 ?

This is what I tried:

Let $$N$$ be the number of possible top 5 : $$N=nCr(100,5)$$

Let $$M$$ be the number of top 5 I'm in : $$M=99*98*97*96*1$$

My chances of being in Top 5 are : $$M/N = 1.2$$

Obviously, this is wrong. What am I missing ?

• The answer is simply $5/100$. – TonyK Mar 7 '19 at 11:30

The correct way to count the number of top5's with you in them is to do what you did for the total number of top5's, except you reserve one seat for you. Then there are 99 players left for the remaining four spots in the top5, so the answer is $$nCr(99, 4)$$.
However, there is an easier way. Consider the entire ranking list for the game. Each possible ranking (among the $$100!$$ possible ones) is equally likely. Particularily, that means that you are equally likely to place in any one of the $$100$$ spots. The probability that you happen to place in one of the top 5 spots is therefore $$\frac5{100}$$.