Question

A pizza parlor offers mushrooms, tomatoes​, and sausages as toppings for the plain cheese base. how many different types of pizzas can be​ made

Answer 1

Answer: 5

Step-by-step explanation:

Given : The total number of toppings for the plain cheese base.= 3

The different types of pizzas can be made by using the 3 toppings is given by using combinations:-

Using 1 topping at a time = $^3C_1$

Using 2 topping at a time =$^3C_2$

Using all 3 topping at a time =$^3C_3$

Also, $^nC_r=\dfrac{n!}{r!(n-r)!}$

Then, The number of different types of pizzas can be made by using the 3 toppings will be :-

$^3C_1+^3C_2+^3C_3\\\\=\dfrac{3!}{1!(3-1)!}+\dfrac{3!}{2!(3-2)!}+\dfrac{3!}{3!(3-3)!}\\\\=1+3+1=5$

Hence, the umber of different types of pizzas can be made by using the 3 toppings =5

Answer 2

3 if 2 each, 4 if you add all of them too