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I am currently running a promotion for my company and we would like to truly explain how many combinations exist for the product. Here is how the steps break down:

  • Step $1:$ Customer orders Rice or Salad version
  • Step $2:$ Customer orders a protein: Chicken, Taco Beef, Steak or Veggie
  • Step $3:$ Customer orders beans: black beans, pinto beans, refried beans (customer may order no beans, 1 bean, 2 beans, all bean options)
  • Step $4:$ Add any or all of these toppings: Shredded Cheese, Pico, Romaine Lettuce Mix, Grilled Onions/Peppers, Fiesta Corn Salsa, Chipotle Citrus Vinaigrette, or Creamy Jalapeno Ranch.
  • Step $5:$ Add any or all of these toppings: Crumbled bacon, Guacamole, Sour Cream, Queso.
  • 0
    Can you solve simpler related problems? For example, if you offered option 1 or option 2, and then option A or option B, how many options would there be?2012-09-17
  • 3
    This question has made me hungry :(2012-09-17
  • 1
    Some of these combinations might be isomorphic. Is the cheese in step 4 different from the queso in step 5?2012-09-17
  • 1
    Does "any or all" choices out of $n$ mean that the number of toppings chosen must be either $1$ or $n$, as a strict interpretation would suggest? And if the more lenient interpretation of "any subset" is applied, why separate steps $4$ and $5$?2012-09-18

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