How many different breakfasts can you have at the local diner?

Question

How many different breakfasts can you have at the local diner if you can select 3 different egg dishes (scrambled, fried, poached),

4 choices of meat (steak, ham, bacon, sausage), 5 breads (white, wheat, rye, muffin, bagel), 6 juices (tomato, grape, apple,

orange, mixed berry, vegetable cocktail), and 4 beverages (water, milk, coffee, tea)?

Answer 1

You would have 3 x 4 x 5 x 6 x 4 = 1440 different breakfast combinations.

Answer 2

Question: How many different breakfasts can you have at the local diner if you can select 3 different egg dishes (scrambled, fried, poached), 4 choices of meat (steak, ham, bacon, sausage), 5 breads (white, wheat, rye, muffin, bagel), 6 juices (tomato, grape, apple, orange, mixed berry, vegetable cocktail), and 4 beverages (water, milk, coffee, tea)?

Answer: Now I'm hungry.

Let's strip away most of the text in the prompt. Keep it simple:

"How many different breakfasts can you have at the local diner if you can select 3 different egg dishes...4 choices of meat...5 breads...6 juices...and 4 beverages...?"

Now it's clear that we have five tasks in this experiment (egg, meat, bread, juice, beverage).

Assuming that a diner must have one of each of these kinds of food and drink (a complete "run" of the experiment), there will be five quantities to multiply. We will use the general multiplication principle.

3 egg x 4 meat x 5 bread x 6 juice x 4 beverage = 1,440 combinations.

Imagine a graph representing the possibilities. 1,440 branches at the end.

You can have 1,440 different breakfasts at the local diner. Sign me up!