Math Is Fun Forum

stvnmsts

Member

Registered: 2008-07-01

Posts: 1

Combinatorial Math question

At least I think it's a combinatorial math question. 

I'm trying to figure out how many possible unique hamburgers I could make given the following options.

4 bun types - English muffin, Reg Hamburger bun, Honey Wheat, no bun
4 meat types - beef, turkey, veggie, chicken
(three weights - 1/3, 2/3, 1 lb)
10 Cheese types
28 Toppings (4 at a time)
18 Sauces

Let's say any one of the unique hamburgers could have mulitple cheeses and sauces but only one bun type and one meat/weight, i.e. No multi meat burgers w/ different meats, no top/bottom bun different, etc.

Does someone have a quick program to knock this out?

Thanks a million.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Combinatorial Math question

If there are 9 cheeses and 1 no cheese, then there are 2^9 = 512 cheesy ways,
or 511 cheesy ways plus 1 no cheese way.

If there are 10 cheeses and 1 no cheese way, then there are
2^10 ways to do cheese including the no cheese way.

---

igloo myrtilles fourmis

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Combinatorial Math question

For the first three parts, you have 4, 4, and then 3 choices.  Each are independent, so you multiply them.  John has done the cheese for you.  For the toppings, out of 28, you choose 4 of them.  Sound like a math function you may be familiar with?  For the 18 sauces, it's using the same method that John used for the cheese.  Multiply everything together and you should get:

263,818,366,156,800

Now just try them all and tell me which one tastes the best.

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."