Four different sets of objects contain 3, 5, 6, and 8 objects, respectively. How many unique combinations can be formed by picking one object from each set?
Let's first answer this by simplifying the question a bit and ask "How many different combinations can be made from 2 different sets of objects - one containing 3 and the other containing 5."
So that gives us Set A with 3 things and Set B with 5 things.
If I pull out the first object from Set A, let's call that Object A1, I can then pull out Objects B1, B2, B3, B4, and B5 - and so can make 5 different unique combinations.
And then I can pull out Object A2 and do it again (so make 5 more unique combinations), and then A3 and do it yet again (for yet another 5 unique combinations).
In the end, we end up with 15 unique combinations.
We can find this number by multiplying the number of objects in A and the number in B:
We can do that with larger numbers of sets and groups as well. For instance, in the question above, we have 4 sets with 3, 5, 6, and 8 objects in them. So the number of unique combinations can be found by multiplying the number of objects in each group together: