How many ways can you order a hamburger?

Inspired by StatsMedic Lesson 4.8

In 2009, Wendy's take-out bag said,"We figured out that there are 256 ways to personalize a Wendy's hamburger. Luckily someone was paying attention in math class." Is this correct?

1. Does the order of the toppings matter? For example, is ketchup then mustard the same as mustard then ketchup? Explain.

2. Wendy's offers 9 topping options for their hamburgers. Choose your three favorite toppings and list all possible ways they can be put in order below. How many possible ways can you put the toppings in order?

Sample: Lettuce (L), Tomato (T), Ketchup (K). LTK, LKT, TKL, TLK, KLT, KTL 6 ways to put the toppings in order

3. How many ways can you order a hamburger with 3 toppings if the order of toppings does not matter?

4. To figure out the total number of ways we can order a hamburger we need to find the number of ways to order 0, 1, 2...8, and 9 toppings. Complete the table below.

# Toppings	Total Ways to Order	# Toppings	Total Ways to Order
0	9C0= 1	5	9C5=126
1	9C1 =9	6	9C6=84
2	9C2=36	7	9C7=36
3	9C3=84	8	9C8=9
4	9C4=126	9	9C9=1

5. What conclusion can you draw about Wendy's claim?

2(1+9+36+84+126) =