Figure Out Possible Combinations

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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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Updated on March 21, 2020

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  • user6673
    user6673 over 3 years

    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!

    • Alex R.
      Alex R. over 11 years
      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.
    • André Nicolas
      André Nicolas over 11 years
      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."