The Combin Function

The Combin function is a mathematical function that is included in Microsoft Excel that provides an easy way of working out how many different possible combinations exist for selecting x items out of y in a certain numerical scenario. For example, if you wanted to find out how many possible ways exist to draw a combination of four cards from a deck of 52, you could use the Combin Function and it would tell you that there are a total of 270 725 possible different combinations of four cards.

How to use the Combin function

To use the Combin function to work out the number of ways of forming various combinations you need to open Microsoft Excel, and then type the following into any cell and press Enter:


Of course, you need to substitute the x and y with whatever values you’re working with, stating the higher value first. In the example mentioned in the paragraph above, where we want to find the number of possible ways of drawing four cards from a 52-card hand, we would type the following:


The mathematics behind the Combin function

Of course, there isn’t a magical creature lurking in the confines of Excel’s source code who rubs a crystal ball each time you use the Combin function and immediately displays your answer. The way Excel works out the answer to whatever numbers you feed into the Combin function is by way of the following mathematical formula:

combin(x,y) = x!/(y!*(x-y)!

As you can see, using the Combin function is a much quicker way to reach an answer than feeding your variables into the more complex mathematical equation above. Simply use the Combin function that is already built into Microsoft Excel in order to quickly work out the number of possibilities that exist for forming a certain combination; for example hands from a deck of cards, or combinations of symbols on slot machines, as well as many other casino-related applications.

View our mathematics of gambling glossary or find out what other topics are covered that relate to the mathematics of gambling – understanding the mathematics behind popular casino games could be the difference between winning and losing!