How to find the most important factors or combination of levels in a finite data set

I’d like to discover which “calendar factors” (e.g. day of the week, month) have the strongest relationship with whether or not a particular product is sold at least once. For days when the product was sold, I have data like this:

Date        Day of Week  Day Type  Month
01-01-2014  Wednesday    Weekday   January
01-13-2014  Monday       Weekday   January
02-09-2014  Sunday       Weekend   February
02-15-2014  Saturday     Weekend   February
02-16-2014  Sunday       Weekend   February
02-23-2014  Sunday       Weekend   February

If we pretend that this is the entire dataset, we see that the product was sold mostly on Sundays in February.

I’ve come up with a simple way to rank each individual calendar factor (e.g. month) as well as a few combinations (e.g. day type + month) by creating a ratio of “sale days” vs. the entire population: using the example data, Wednesday + January would have a rank of 1 / 5. However, I’m struggling to determine which factors and/or combination of factors are most significant without simply picking the highest-ranking one.

I feel like there must be a stronger mathematical approach to solving this kind of problem. Any ideas? Also, how would you classify this problem?