Question 625175: Please help me understand how to calculate this.
Take any Subway restaurant as your experimentation site. Determine the different types of breads, meats, salads, toppings, etc. Find out how many different ways of producing a sandwich/roll. State your assumptions (For example, every sandwich has to have one type of bread but may not include meat).
11 different ‘vessels’ (Flatbread, or a half or whole of five different breads)(Assume 1 per sandwich)
4 cheese choices(Assume 0 to 4 per sandwich)
Toasted or not
Add bacon or not
9 different veggies (can range from 0 to any combination of the nine)
9 different sauces (can range from 0 to any combination of the nine)
Thank you!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I suspect they asked you how many different sandwiches can be made. (You do not say).
It is a weird situation, with a lot of possible options.
Some monster sandwiches can be generated.
Your problem hints about 11 different choices for the bread. (I imagine flatbread has just one option, but for the other 5 types of bread you can use one of half. Online, I saw 10 options, including flat bread and four types of roll in 6-inch or foot long sizes).
Then, there are options for the filling flavor. Online, I saw 5 breakfast-type flavors. I would ignore those to make it simpler. There were 20 options for flavor for lunch-type sandwiches, including "veggie delite" and 19 with some type of meat. I would stick to those 20 options.
There are more choices that are yes/no type:
bacon?
onion?
lettuce?
tomato?
bell peppers?
cucumbers slices?
.......
mayo?
lite mayo?
oil?
ranch?
chipotle southwest?
honey mustard?
mustard?
.....
Your problem talks about 9 veggie choices and 9 sauce choices. Online, I saw 9 sauces, but only the 5 veggies I listed above.
If you had 9 veggie choices and 9 sauce choices, and you could ask for none or as many as you wish, there would be 2 possibilities for each choice: yes or no.
That would give you  possibilities.
All choices multiply the possibilities.
Coupling those "fixings" possibilities with 20 filling flavors, and 11 bread choices, plus 2 choices (yes or no) for toasting, the possibilities are
That's about 100 million possible sandwiches.
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