0

How do I calculate how many combinations I can create with a set amount of categories and within each category, there are different amounts of objects. For example, if I have 5 categories (1,2,3,4,5) and within each category, there are different amounts of objects (cat1: 4, cat2: 5, cat3: 6, cat4: 7, cat5: 8), how many combinations can I make without changing the order? Like a combination lock with 5 digits, but each tumbler has different amounts of variables.

Sorry for my bad math language.

MathNoob
  • 1
  • https://en.wikipedia.org/wiki/Rule_of_product – JMoravitz Mar 28 '22 at 14:36
  • 2
    The rule of product in the context of combinatorics loosely paraphrases as "If you wish to count the total number of outcomes to a scenario and each outcome can be uniquely described via a sequence of steps with choices such that the number of options for each step does not depend on previously made choices (though the options themselves may change so long as the number of options does not) (uniquely meaning each outcome is described exactly once, no more and no less), then the total number of outcomes is the product of the number of choices available at each step" – JMoravitz Mar 28 '22 at 14:39
  • Here, $4\times 5\times 6\times 7\times 8$ total outcomes. – JMoravitz Mar 28 '22 at 14:39

1 Answers1

0

Try looking at all the categories and how many choices you have, then multiply them. To use your example:

Category 1 has 4 objects, so you have 4 choices. Category 2 has 5 objects, so you have 5 choices. This means that you have $4\cdot5=20$ choices in categories 1 and 2.

If you do this for all categories you would have $4\cdot5\cdot6\cdot7\cdot8=6720$ choices overall.

JanTheMan
  • 98