Question

At the local burger palace, you can order a hamburger with the following “extras’: tomato, lettuce, bacon, onion, or cheese. How many different ways can you order a burger if you always order one with three different “extras” on it?

Answer 1

Answer:

10 ways

Explanation:

The number of ways to select x elements from a group of n elements is calculated as

$\text{nCx}=\frac{n!}{x!(n-x)!}$

These ways are called combinations. In this case, we need to select 3 different extras from a group of 5 extras ( tomato, lettuce, bacon, onion, or cheese). So, the number of ways to make an order is

$5C3=\frac{5!}{3!(5-3)!}=\frac{5!}{3!\cdot2!}=10$

Therefore, the are 10 different ways to order a burger with three different extras.