# Subsets in a set formula

Use the formula for the number of subsets of a set with n elements to solve the problem.

1. Pasta comes with tomato sauce and can be ordered with some , all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli,shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for ordering pasta with tomato sauce.

2. A village has 4 fire engines. If a radio dispatcher receives a call, depending on the nature of the situation,no engines, one engine, two engines, three engines, or all four engines can be sent to a fire . How many options does the dispatcher have for sending the fire engines to the scene of the caller?

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#### Solution Preview

The number of subsets of an n element set is 2^n since each element is either included in the subset or it isn't.

1. Pasta comes with tomato sauce and can be ordered with some , all, or none of these ingredients in the sauce: {onions, garlic, ...

#### Solution Summary

This provides examples of using the formula for number of subsets of a set to solve counting problems.