Need help on a business math problem involving factorial calculation.

Question

I am attempting to solve a real problem for my business. We own a chicken wing sports bar. We offer four Styles of wings based on cooking/prep type...Fried Naked, Fried Breaded, Smoked and Roasted. When a customer orders one of those types, they can choose from 24 sauces AND they can choose up to two sauces per order. For example a customer can order 10 Smoked wings with 5 wings sauced with Buffalo sauce and 5 wings covered in Teriyaki sauce. Obviously a customer might also order 10 Smoked wings and choose to have all 10 in one sauce like Buffalo (which is what makes the math more than we can accurately calculate).

What we are trying to calculate for our advertising is....how many possible combinations of choices does this offer our customers?

We would appreciate any help the universe can provide!

Thanks

Answer 1

The basics of the problem are manageable with regard to the number of types of wings and selection of sauces.Once you move to the individual number of sauces on a particular number of wings in the mix, there is not enough information given.

For example, how many wings can you get per order, 10 or 15 or 20 etc. You would need to know this before all your questions are answered.

As far as the basic problem concerning just the type of wings and the flavors, the number of combinations would be

Combinations = 4*₂₄C₂ = 1,104 ways to order wings and sauces (but does not include the number

of wings per order have which sauce)