# 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?

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Jul 6, 2016

$3 \cdot 5 \cdot 6 \cdot 8 = 720$

#### Explanation:

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: $3 \cdot 5 = 15$

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:

$\left(\text{Set A")("Set B")("Set C")("Set D}\right)$

$3 \cdot 5 \cdot 6 \cdot 8 = 720$

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