Chapter 12.6, Problem 1P

a.

To determine

To calculate: The number of pizzas one can order with one meat topping and one vegetable topping .

Answer to Problem 1P

The number of pizzas are $48$ .

Explanation of Solution

Given information:

8 vegetable toppings and 6 meat toppings.

Formula used:

When events are independent, the number of outcomes can be found out by Multiplication Counting Principle.

If there are m ways to make a first selection and n ways to make a second selection then there are $m\times n$ ways to make the two selections.

Calculation:

Consider ,

Number of vegetable toppings - 8.

Number of meat toppings - 6.

Therefore, pizzas with one meat topping and one vegetable topping are-

  $\text{8 vegetable toppings }\times 6\text{ meat toppings }=48\text{ pizzas}\text{.}$

Hence, the number of pizzas are $48$ .

b.

To determine

To show: whether the tree diagram a convenient way to find the answer to part (a).

Answer to Problem 1P

Yes, we can use tree diagram.

Explanation of Solution

Given information:

8 vegetable toppings and 6 meat toppings.

Formula used:

When events are independent, the number of outcomes can be found out by Multiplication Counting Principle.

If there are m ways to make a first selection and n ways to make a second selection then there are $m\times n$ ways to make the two selections.

Calculation:

Consider ,

Number of vegetable toppings - 8.

Number of meat toppings - 6.

Vegetable toppings Meat toppings 1veg and 1meat toppings

8 6 1veg 1meat

2veg 1 meat

1veg 2 meat

And so on.

Hence, with the tree diagram we can order pizza with different toppings . The number of ways are 48.

This implies we can use tree diagram for part (a).