Question

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 A1 never orders a sandwich with a ham/cheddar cheese combination nor a sandwich with a white bread/chicken combination, how many different sandwiches could A1 order?

Answer 1

The answer to the question is;

The number of different sandwiches A1 could order is 111 different sandwiches.

Explanation:

The number of kinds of bread available = 4

The number of kinds of meat available = 6

The number of kinds of cheese available = 5

Total number of ways a sandwich can be ordered is given by

4 kinds of bread × 6 kinds of meat × 5 kinds of cheese = 120 ways

However, the customer A1 never orders a sandwich with a ham/cheddar cheese combination nor a sandwich with a white bread/chicken combination.

This means that we need to look for the number of ways to order a sandwich with a ham/cheddar cheese combination and a sandwich with a white bread/chicken combination and subtract them from the total number of possible ways to order a sandwich as follows.

The number of ways to order a sandwich with a ham/cheddar cheese combination is given by;

First we order bread in 4 ways then we order ham in one way then we order cheese the cheddar cheese, that is 1 way. So we we have

4 × 1 × 1 = 4 ways

Also The number of ways to order a sandwich with a white bread/chicken combination is given by;

First we order bread in 1 way, which is white bread, then we order chicken in 1 way then we order cheese in 5 ways. So we we have;

1 × 1 × 5 = 5 ways

Therefore we subtract 5 + 4 = 9 from 120 which gives

120 - 9 = 111 ways

A1 could order 111 different sandwiches.