Old World Subs offers 6 types of bread 22 types of meat 12 t

Old World Subs offers 6 types of bread, 22 types of meat, 12 types of cheese, a choice of mustard, mayonnaise, both or neither, and a choice of lettuce, tomato, or neither for their sandwiches. Is it mathematically valid for them to advertise \"hundreds of sandwiches to choose from?\" Show why or why not.

Solution

The number of ways making sandwiches

Choosing 1 bread from 6 = 6C1 = 6 ways

Choosing 1 meat from 22 = 22C1 = 22 ways

Choosing 1 cheese from 12 = 12C1 = 12 ways

Mustard, Mayonaise, Both or Neither = 4 ways

Choosing Lettuce, Tomato, Both or Neither = 4 ways

Therefore total no of sandwiches = 6*22*12*4*4 = 25,344 sandwiches to choose from.

Therefore it is mathematically valid to advertise hundreds of sandwiches to choose from.