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?

 May 23, 2020

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.

 May 23, 2020

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