how many different pizzas can be made with 10 toppings

[erfugate]

I have a problem solving question

you have ten pizza toppings how many different pizzas can you make

I know there will be one 1 top, and ten 2 top after that i am not sure on where to start any hints or ways to help would be greatly appreciated

 

[erfugate]

Re: i need help please!!

Will there be more or less 3 topping pizzas than there were 2 topping?? :?

 

[Denis]

Re: Pizza?!?!?

10C0 + 10C1 + 10C2 ..... + 10C9 +10C10

10C0 = 1 : 1 way with no topping.

> Will there be more or less 3 topping pizzas than there were 2 topping??
10C2 = 45, 10C3 = 120

If you do not understand that, then you were not ready for this question: see your teacher.

 

[erfugate]

Re: Pizza?!?!?

that makes no sense to me but i understood it as this you have 2 choices either have the topping or don't, and there are 10 toppings so you ask your self that question 10 times 10 times so i took 2 raised to the tenth power and got the answer of 1024 different pizzas

 

[pka]

Re: Pizza?!?!?

that makes no sense to me but i understood it as this you have 2 choices either have the topping or don't, and there are 10 toppings so you ask your self that question 10 times 10 times so i took 2 raised to the tenth power and got the answer of 1024 different pizzas

Did you know that \(\displaystyle 2^{10} = \sum\limits_{k = 0}^{10} {{10} \choose {k} }\)?