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I am trying to figure out how many possible of combinations I can have between two sets of values. My two sets looks like this:

Set 1: [White, Black] Set 2: [Blue, BlueGreen, Brown, Orange, Pink, Purple, Red, Yellow, YellowGreen]

Set 1 has two options. Set 2 has ten options. Someone must pick one option from each set. How do I figure out how many potential combinations there are? I'm not sure if I need to do 2 * 10 and then use permutations. Or if I should do 2! then add it to 10!.

Thank you for your help!

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Ask the following: for each particular element of set 1, say "White", how many combinations can you make by picking elements from set 2, e.g. "White,Blue", "White, BlueGreen" etc.? Then think about whether you need to add or multiply the results for each element of Set1. – Alex R. Mar 20 '12 at 19:30
I count $9$ in set $2$. But assume $10$, add Violet. Combinations is perhaps too abstract. If we are only going to wear pants and shirt, and have $2$ pants (white, black) and $10$ shirts, then there are $2\cdot 10$ "outfits." – André Nicolas Mar 20 '12 at 19:34
up vote 0 down vote accepted

If you pick one item from each set, you have two choices for the first and ten for the second, $2*10=20$ in all. If you pick all the items from the first set in a particular order and all the items from the second in a particular order you have $2!*10!=7257600$

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