A charter school assigns seats by conducting a lottery. In the past, each child was given a number, and balls were selected randomly. This year, they are starting a new policy of giving low-income students 3 balls, and other kids 2 balls. 

They have 10 seats to assign, and 31 applications. I don't know how many students are low-income, but let's assume 12.

How is the number of low-income students likely to be changed by the new policy? Is there a way to create a formula where I could plug in the number of low-income students and see the probability distribution?