Question

Papa Your Mommas Pizza Parlor has 6 meat toppings and 7 vegetable toppings from which to select. The parlor has three different sizes of pizza (individual, large, and giant) and two different types of crust (deep-dish and thin).

(a) How many different two-topping pizzas could be ordered?

(b) How many different two-topping pizzas could be ordered with exactly one meat topping and exactly one vegetable topping?

(c) How many different four-topping vegetarian pizzas could be ordered?

The answers are

a) 468

b) 252

c) 210

I just need the work

Answer 1

(a)

Case 1: 1 Meat & 1 Vegetable:

1 Meat can be selected from 6 Mean in 6C1 = 6 ways

1 Vegetable can be selected from 7 Vegetable in 7C1 = 7 ways

Sizes = 3

Types of crush = 2

So,

Number of two-topping pizzas could be ordered with exactly one meat topping and exactly one vegetable topping = 6 X 7 X 3 X 2 = 252

Case 2: 2 Meat

2 Meat can be selected from 6 Mean in 6C2 = 15 ways

Sizes = 3

Types of crush = 2

So,

Number of two-topping pizzas could be ordered with exactly two meat topping = 15 X 3 X 2 = 90

Case 3: 2 Vegetable:

2 Vegetable can be selected from 7 Vegetable in 7C2 = 21 ways

Sizes = 3

Types of crush = 2

So,

Number of two-topping pizzas could be ordered with exactly exactly two vegetable topping = 21 X 3 X 2 = 126

So,

Number of different two-topping pizzas could be ordered = 252 + 90 + 126 = 468

So,

Answer is:

468

(b)

1 Meat can be selected from 6 Mean in 6C1 = 6 ways

1 Vegetable can be selected from 7 Vegetable in 7C1 = 7 ways

Sizes = 3

Types of crush = 2

So,

Number of two-topping pizzas could be ordered with exactly one meat topping and exactly one vegetable topping = 6 X 7 X 3 X 2 = 252

So,

Answer is:

252

(c)

4 Vegetable can be selected from 7 Vegetable in 7C4 = 35 ways

Sizes = 3

Types of crush = 2

So,

Number of different four-topping vegetarian pizzas could be ordered = 35 X 3 X 2 = 210

So,

Answer is:

210