The deli has four kinds of bread, six kinds of meat and five kinds of cheese. A sandwich consists of one type of bread, one type of meat and one type of cheese. Ham, chicken, cheddar cheese and white bread are each offered at the deli. If Al never orders a sandwich with a ham/cheddar cheese combination nor a sandwich with a white bread/chicken combination, how many different sandwiches could Al order?
+23246 Since there are 4 kinds of bread, 6 kinds of meat, and 5 kinds of cheese,
there are a total of 4 x 6 x 5 = 120 different sandwiches.
However, we need to exclude a ham/cheddar cheese combination. Since we can have this
with any kind of bread there are 4 sandwiches excluded.
We also need to exclude a white bread/chicken combination. We can have this with any
kind of cheese, so we have to exclude these 5 sandwiches.
There are 120 - 4 - 5 = 111 sandwiches remaining.
