## Trying to design an optimal genetic experiment

I have a dish full of cells. I have ten genes. Three of these genes in combination will make the cells turn green if they get inside the cell (I need all three at once, but since there are many copies of the ten genes, each cell may contain more than one copy of each gene). So in this experiment, I will add all of the genes to the dish, then I will examine only the green cells. Then I remove all of the genes from the green cells, and I can get approximate ratios of each gene in the total green cell population, in order to tell which genes were successful. The key here is that I can control the probability of each gene getting inside each cell. (For example, if I chose a probability of 0.1, then there would be a 10% chance of each factor getting inside of the cell). So at the end, for every hundred green cells, there will be a number of copies of each gene. The number of copies of each of the three successful genes will be the same, and the number of copies of each of the unsuccessful genes will be the same. I would like to know the ratio of successful to unsuccessful genes. I need a formula for this because I would like to make an Excel spreadsheet where each column has a different probability of the factor getting into the cell "X", and each row has the number of successful factors needed "Y" (in this example, I told you it was three, just for the sake of simplicity). Thanks for any help.