imagine you are the owner of a pizza shop that offers three different types of crusts, seven different toppings, and three different cheeses. Create an advertisement for your shop listing all the choices you offer and advertising a three-topping pizza with one type of cheese for $9.99How many different combinations of 1 crust, 3 different toppings, and 1 cheese does your shop offer?Of the possible combinations you offer, which is your favorite?What is the probability that a person would order your favorite pizza at random?

Question

amistre64 · Answer

what are your thoughts?

anonymous · Answer

I'm soooo lost

amistre64 · Answer

3 choose 1
7 choose 3
and
3 choose 1

right?

amistre64 · Answer

3 crusts; 3 choose 1 ways to order 1 crust

7 toppings; 7 choose 3 ways to order 3 different toppings 

3 cheeses;  3 choose 1 ways to order 1 cheese

amistre64 · Answer

how do we calculate these?

amistre64 · Answer

crusts:  a,b,c

we can order a, b, or c ... 3 ways to order a crust
-------------------------

cheese, x,y,z ; combine with the crusts gives us

ax, bx, cx, ay, by, cy, az, bz, cz

we can order 3 crusts and 3 cheeses in 9 different ways

$$\binom31\binom31=9$$
$$\binom31\binom31\binom73=?$$

amistre64 · Answer

its a brute to try to define all the ways to order 3 toppings out of 7, which is why we have a formula to help out
$$\binom nk=\frac{n!}{k!(n-k)!}$$

amistre64 · Answer

ive got to go, but these are the basics for you