I work at a pizza place and was discussing a scenario with my

>>7734870

This is a simple combination problem because mushroom/tomato is the same as tomato/mushroom. There are [math]C(50, 50)[/math] ways to choose 50 toppings from 50, there are [math]C(50, 49)[/math] ways to choose 49 toppings from 50, etc.

>>7734874

3x2x1 gives 6 different pizzas with 3 topping choices but in reality the answer is 7 because you can have each topping on it's own too.

>>7734885

With three topping choices you can either choose three toppings or choose two toppings or choose one topping. There are [math]C(3,3)[/math] ways to choose three toppings, [math]C(3,2)[/math] ways to choose two toppings, and [math]C(3,1)[/math] ways to choose one topping. That means there are
[eqn]C(3,3) + C(3,2) + C(3,1) = 7[/eqn]
ways to choose toppings.

Your factorial answer [math]3 \times 2 \times 1[/math] is not correct. It's a combination problem.

>>7734890

Sorry I don't know what the C(3,3) etc means.

>>7734894

So go look it up.

>>7734870
There are 2^50 - 1combinations if you want to avoid the "empty topping".
From 1 up to 50 toppings at once.
This is roughly 10^15

>>7734897
I don't know what to look up. Can you just tell e what that means to equal 7?

http://www.rapidtables.com/math/number/exponent/multiplying-exponents.htm

>>7734894

like a dude working in a pizza place is just gonna know what a combinatorial number system is.

>>7734897
I literally study statistics and I've never seem this C function before either

>>7734901

I'd say this is correct.

I calculated it as c(50, 50) + c(50, 49) + c(50, 48) + ... + c(50, 0) which turns out is the same as 2^50, but im not sure about the -1.

So there are about 1,125,899,906,842,624 different options.

So when you go into work next time, go tell your boss that there are exactly one quadrillion one hundred twenty five trillion eight hundred ninety nine billion nine hundred six million eight hundred forty two thousand six hundred twenty four different combinations of toppings in your pizza place.

Bonus points if you can remember it by heart :)

>>7734926

What is going on in the brackets?

>>7734926

Lol the reason we ever were discussing it was becasue this guy was looking at the menu for 20 minutes and he just got a cheese and pep pie.

>>7734928
it's called "n choose k"; a way of expressing / calculating the number of unique combinations whenever choosing k elements from a set of size n.

https://en.wikipedia.org/wiki/Combination

>>7734916
Wow. What shithole do you study at?

>>7734943
This. I don't even study that career and I have obviously seen it. Shit even my casio calculator has that function.

>>7734937

great

finally figured it out!

>>7734943
I can obviously tell from the context what it is.
We put it between parentheses, like a 2x1 vector

You would have

2^49 + 2^48 + 2^47 ... + 2^0 = Amount of topping combinations

You would also have to +1 in case you count having no toppings at all as a possibilty.

In your example with three toppings you would have
2^2 + 2^1 + 2^0 = 7 topping combinations
and it would be 8 if having no topping at all is an option for you.

>>7735107
That equals 2^50.

Look, each topping is either on a pizza or not on it. Two options per topping. Multiply by 2 for every on available... so multiply by 2 50 times... so it's 2^50. If you want to exclude the empty pizza, it's 2^50 - 1.