34 million pizzas at 50% OFF

Here is a delicious math happening!!! Right now you can order any pizza from Dominos for 50% off and in their  TV Commercial, they boast ’34 Million Ways’- Wow! https://www.ispot.tv/ad/wNNF/dominos-34-million-combinations 

Problem Posed: How did they combine all options to get to the total number of possible combinations as 34 million?

50off

Information needed: This is what I found on the website as

AVAILABLE OPTIONS

Pizza Crusts (5 options)

  1. Hand Tossed
  2. Handmade Pan
  3. Crunchy Thin Crust
  4. Brooklyn Style
  5. Gluten Free Crust

Pizza Sizes (3 options)

  1. Small (10″)
  2. Medium (12″)
  3. Large (14″)

Sauces (9 options)

  1. Alfredo Sauce
  2. BBQ Sauce
  3. Blue Cheese Sauce
  4. Garlic Parmesan White Sauce
  5. Hearty Marinara Sauce
  6. Hot Sauce
  7. Mango Habanero Sauce
  8. Ranch Dressing
  9. Robust Inspired Tomato Sauce

Meats (8 types yes-no)

  1. Bacon
  2. Beef
  3. Ham
  4. Italian Sausage
  5. Pepperoni
  6. Philly Steak
  7. Premium Chicken
  8. Salami

Non-Meats (17 types- yes or no)

  1. American Cheese
  2. Banana Peppers
  3. Black Olives
  4. Cheddar Cheese
  5. Cheese
  6. Diced Tomatoes
  7. Feta Cheese
  8. Green Pepper
  9. Jalapeno Peppers
  10. Mushrooms
  11. Onions
  12. Pineapple
  13. Roasted Red Peppers
  14. Shredded Parmesan
  15. Shredded Provolone Cheese
  16. Sliced Provolone
  17. Spinach

A pizza commercial claims that you can combine their ingredients to 34 million different combinations. I was curious!   I thought about combinatorics skills and tried to figure it out. From their website, I was able to get this info:

  1. crust (5 types, choose 1)
  2. size (3 types, choose 1)
  3. sauce  (9 types, choose 1)
  4. meats (8 types, choose up to 8) 2^8=256
  5. non-meats (17 types, choose up to 18) 2^17=131,072

How did they combine all these to arrive at the total number of possible combinations as 34 million?

Making assumptions: Let’s assume that we were only considering toppings.

Do the Math: 34 million is closest to 2^25 so maybe they were only counting the meat and non meat toppings.

33,554,432 pizza combinations

Revise my model: But if you play with the sauces, you would have lots more 🙂
33,554,432*9=  301,989,888
See related math happening http://mathhappenings.onmason.com/2017/02/12/pascals-pizza-pizzazz/