Chapter 4.2, Problem 44HP

To determine

To find: The correct option.

Answer to Problem 44HP

The correct option is B.

Explanation of Solution

Given:

The number of meat topping offered is $5$ .

The total number of vegetable is $6$ .

The selected number of meat topping is 1 and vegetable topping is $2$ .

Calculation:

Consider the total number of meat toping is 5 then, the number of way in which it is selected is,

  $\begin{array}{c}{}^5{C}_1=\frac{5!}{1!\left(5-1\right)!}\\ =\frac{5!}{1!4!}\\ =5\end{array}$

The number of ways in which the vegetable topping is selected is,

  $\begin{array}{c}{}^6{C}_2=\frac{6!}{2!\left(6-2\right)!}\\ =\frac{6\times 5\times 4!}{2\times 1\times 4!}\\ =15\text{ways}\end{array}$

Then, the number of types of pizza that can be ordered is,

  $5\times 15=75$

Thus, the correct option is B.