The canteen sells sandwiches on white, brown, or grain bread. The filling can either be egg, cheese, chicken, or ham. These can be served with tomato sauce, BBQ, or no sauce. How many different types of sandwiches are available at the canteen?
2 Answers
HINT:
It is sometimes easier to see the solution if you work on a problem like this backwards.
Suppose you already have a white bread sandwich with egg filling, then how many sauces can you choose from? Three, right? If you had chosen cheese for example, you would still have three sauce choices. So this means that if you choose white bread, then you have $4\times 3$ choices of fillings and sauce.
Now, how many types of bread can you choose from?
Note that choices are independent of each other, so you can have any choice of bread with any choice of filling and any sauce.
That means that we can work with choices of bread etc independently. Suppose you only choose bread, how many choices are there? There are three. After you've chosen bread you can choose fillings, how many choices of fillings are there? There are four. So how many choices of bread AND fillings are there? How can you proceed to sauces?