Chapter 0.1, Problem 1E

To determine

To calculate:How many different pizzas can be ordered with one cheese and one topping.

Answer to Problem 1E

16 pizzas can be ordered with one cheese and one topping.

Explanation of Solution

Given information:we need choose only one cheese and one topping at a time

Therefore,

• Choose of crust = 2
• Choose of cheese = $C_1^2$
• Choose of topping = $C_1^4$

Hence, according to the fundamental counting principle (FCP), the total number of ways of ordering a different pizza is $=2\times C_1^2\times C_1^4$

Formula used: $C_r^n=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

  $=2\times \frac{2!}{1!\left(2-1\right)!}\times \frac{4!}{1!\left(4-1\right)!}$

  $=2\times \frac{2\times 1}{1\times 1}\times \frac{4\times 3!}{1\times 3!}$

  $=2\times 2\times 4$

  $=16$