I have $100$ balls and on each ball is labelled a number between $1$ and $100$. No two balls can have the same number, so the interval $1\ldots 100$ is represented by the balls.
I now pick 20 balls at random, one by one without putting them back at any point. I am trying to find the probably of getting 4 certain numbers. The sequence of these 4 numbers does not matter.
Here is my solution: The first time I pick up a ball the probably is $1/100$. The next time it is $1/99$, etc.. So the total probably of getting the four desired numbers is $1/(100\cdot 99\cdot 98\cdot 97)$.
Is this correct?