Question

A chicken restaurant offers a meal combination where the customer can select from the following side dishes

-Mashed potatoes

-Potato wedges

-Baked beans

-Cole slaw

-Corn

-Green beans

-Macaroni and Cheese

Based on the fact that the customer can choose 3 side dishes with their meal, the restaurant launched an aggressive advertising campaign saying that the customer had an amazing 343 choices for their side dishes… This, of course, was determined by noting that for each side, there were 7 choices, and then having a choice of 7 sides for each of the remaining two sides, giving 7x7x7 or 343 choices.

1.) There was a mathematical flaw found in this logic, giving a number of choices much larger than what the actual total should be. Determine why this calculation is incorrect.

Knowing that the above determination is incorrect, we might wonder how many meal choices are possible. A customer can choose a total of 3 side dishes from the 7. Repeats, however, are allowed. Customers can choose to have two mashed potatoes and a corn, for example.

2.) Determine the total number of ways a customer can choose a 3-side dish meal.

Answer 1