There is a list of $63$ items, from which $20$ items are picked in month $1$. What is the chance of $1$ item from the $20$, being picked again in the month $2$?(month $2$ also picks 20 items)
Then further, what is the chance that $2$ items from the $20$ from month $1$ are picked again in month $2$.
Then further, what is the chance that $3$ items from month $1$ are picked again in month $2$..... etc... in theory all the way to the probability of picking all $20$ items identically from month $1$ to month $2$ out of a total of $63$.
My goal is to able to do this for any number, such as the chance that $9$ items from month $1$ are picked again in month $2$.
From my understanding, the chance of getting 1 item the same from $20$ items picked from a total of $63$ from month $1$ to month $2$ is:
$$1 - \frac{_{43}C_{20}}{_{63}C_{20}}$$ or $99.99$%