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I have a quick question. I'm terrible at math so when I read the other posts on this it made no sense to me. I'm creating a trading card game, and I need to know how many possible UNIQUE cards my card generator can produce.

  • Each card MUST have a random percent bonus from 1 to 100.
  • It's possible to have a percent bonus but no color bonus.
  • Each card can have either no color bonus or up to four color bonuses.
  • Whenever there is a color bonus there Must be a sub-type with it
  • There are four color types. (red, blue, green, purple), 4 in total.
  • Each color has 20 sub types. (drain, dodge, frost, Revive...), 20 in total.
  • The color types and sub-types are chosen at random

    Example:
    1% bonus [none(none), none(none), none(none), none(none)]
    1% bonus [red(drain), none(none), none(none), none(none)]
    1% bonus [red(dodge), none(none), none(none), none(none)]
    1% bonus [red(frost), none(none), none(none), none(none)]
    ... 
    100% bonus [red(revive), blue(revive), green(revive), purple(revive)]
    

Thanks

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Think of the color options as $4$ slots with "nothing" being a possible subtype. Selecting that option in, say, the blue slot would simply mean that there was no blue bonus attached to that card. By the specified terms you could choose "nothing" in all $4$ slots or in any subset. Viewed this way, there are $21$ possible subtypes in each of the four slots which may be chosen independently. Combining that with the $100$ options for the percent bonus we see that there are $$100(21)^4=19,448,100$$ possible cards.

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