Probability that 433 people win at the same time in 6/55 grand lotto

Winning a lottery seems impossible especially when we look at it from a point of view of probability. But what is exactly the probability that 433 people wins a lottery just like what happened in the Philippines' 6/55 Megalotto?

Lets solve it in the name of the Gods of probabilities. 

Problem: 

What is the probability that 433 people win the jackpot price in 6/55 Megalotto? 

Solution: 

First, we solve for the number ways to choose 6 digits combinations from 55 numbers. 

You guessed it right! It is 66C5 or 8,936,928. So the probability of winning is 1/8,936,928.

Now, think that 433 people standing side by side. Each of them has a probability of 1/8,936,928 of picking the winning number. 

The probability that two persons picked the winning number will be the product of these probabilities. So  1/8,936,928.

Now, what is the probability that 3 people pick the winning combination? Right! It is 1/(55C6)^3, where ^ denotes exponentiation. 

From this, we can generalized that the probability that n number of people pick the winning number will be, 

Using this formula, the probability that 433 people wins the jackpot price will be, 

I can't even fathom how small this number is. We can't solve the exact numbers because it is very, very, very, very small. However, we can determine how small this number is. When you input this in a calculator it is reported as 0.