I'm trying to make a system to calculate the Multivariate Hypergeometric Distribution in Trading Card Games. The equation:
In this scenario I have a deck consisting of 60 cards. In this deck I have several group of cards I need to have together to make certain comboes. I have labled such card groups as F, E and P
In my 60-card deck I have the following ratio:
- 3 cards in Group F
- 4 cards in Group E
- 5 cards in Group P
- 48 "other" cards not belonging to any of the above groups**
The objective is to draw 10 cards in the beginning of the game and calculate the probability of the 10 cards containing:
- at least 1 card in Group F
- at least 1 card in Group E
- at least 1 card in Group P
This of course means that the remaining 7 cards would consist of either F, E, P or some of the 48 "other" cards.
I know how to solve this mathematically but it is quite a process to do over and over, so is it possible to use Google Sheets to solve this, given that F, E and P are variables which will be solved through multiple steps (essentially finding P first, then E and finally F)?