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Question 58

A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is

Solution

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Number of ways to choose a sandwich = $$^5C_1$$ ways

Number of ways to choose a bread = $$^4C_1$$ ways

Number of ways to choose bread size = $$^2C_1$$ ways

Number of ways to choose sauces = $$^6C_0+^6C_1+^6C_2=1+6+15=22$$ ways

So, number of different ways = $$^5C_1\times\ ^4C_1\times\ ^2C_1\times\ 22=5\times\ 4\times\ 2\times\ 22=880$$ ways.

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