Chapter 0.4, Problem 15E

To determine

To find: whether its permutation or combination.

Answer to Problem 15E

15 different toppings can be made with 2 choices and 6 toppings.

Explanation of Solution

Given information:

Different two-topping pizzas can be made if there are 6 options for toppings.

Calculation:

Here we have 6 toppings and 2 choices.

This is a combination problem because order does not matter, key word is “choosing”.

The required formula is $\frac{n!}{k!\left(n-k\right)!}$ , where n is the number of possibilities and k is the number of choices.

So, we get

  $\begin{array}{c}\frac{6!}{2!\left(6-2\right)!}=\frac{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{\left(2\cdot 1\right)\left(4\cdot 3\cdot 2\cdot 1\right)}\\ =\frac{30}{2}\\ =15\end{array}$