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

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

Answer 2

Answer: 5

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=(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\\\\=(3!)/(1!(3-1)!)+(3!)/(2!(3-2)!)+(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