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Suppose you have three small decks of cards

[A,B]

[C,D]

[E,F]

How many unique combinations can you make following the rules that

  1. Limited to 3 cards
  2. Each deck must be used
  3. Only one card from each deck

ACE ACF ADE ADF BCE BCF BDE BDF

What formula would be used to determine this?

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    I've tried doing it by hand, which works for this small set. I took this math ~10 years ago, so all I remember is combinations using factorials, but I don't remember the rest of the maths.. The fact that 2! * 2! *2! works is probably luck.. right? – 2017-01-14
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    OK. Let's start from (1). How do we formulate that question in terms of combinations? Can we think of merging the three mini-decks and picking three cards from six? How many ways do we have of doing that? – 2017-01-14
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    How many choices can you do in the first deck? And for the second? And for the third? Because all cards are different every hand is unique, hence the possible hands (of three cards) are $2\cdot 2\cdot 2=8$. – 2017-01-14
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    In this particular scenario, we cannot merge the decks. A and B cannot be chosen together, (same for C and D, E and F). – 2017-01-14

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