164,640 Possible Combinations
Create Your Perfect Sandwich: 164,640 Mouthwatering Combinations Await Your Imagination
Stoby's opened its doors on July 21, 1980, with just one item on the menu: The Stoby Sandwich. If you were to launch a restaurant with only one menu item, a sandwich offering 164,640 possible combinations would be a good choice. The Stoby Sandwich remains the top-selling item on our menu.
The Math
Teacher said to show our work.
How many ways can you build a Stoby Sandwich?
Bread: choose 1 of 5
= 5
Meat: choose 3 portions from 6, and you can double or triple up
CR(6,3) = C(8,3) = (8 × 7 × 6) ÷ (3 × 2 × 1)
= 56
Cheese: choose 2 portions from 6, and you can double up
CR(6,2) = C(7,2) = (7 × 6) ÷ (2 × 1)
= 21
Condiments: choose at least 1 of 3
C(3,1) + C(3,2) + C(3,3) = 3 + 3 + 1
= 7
Toppings: choose any of 2, or none
C(2,0) + C(2,1) + C(2,2) = 1 + 2 + 1
= 4
Multiply the categories:
5 × 56 × 21 × 7 × 4
5 × 56 = 280
280 × 21 = 5,880
5,880 × 7 = 41,160
41,160 × 4 = 164,640
164,640 possible Stoby Sandwiches.
And btw, you can choose Ruffles, Cheetos, substitute fries, or order it without chips, and with or without a pickle spear:
164,640 × 4 × 2 = 1,317,120
So in fact, there are 1,317,120 ways to order a Stoby Sandwich.
