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You are at a sandwich shop. You can choose from white or rye bread, turkey or ham, and Swiss or American cheese to make your sandwich. All eight possible sandwich combinations are listed below. If we take sandwiches and as a subset of the sample space, which of the statements below describe this subset?

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Find probabilities using combinations and permutations

Full solution

Q. You are at a sandwich shop. You can choose from white or rye bread, turkey or ham, and Swiss or American cheese to make your sandwich. All eight possible sandwich combinations are listed below. If we take sandwiches and as a subset of the sample space, which of the statements below describe this subset?

Calculate Total Combinations: Identify the total number of sandwich combinations. $\newline$ Calculation: $2$ types of bread $*$ $2$ types of meat $*$ $2$ types of cheese = $2 * 2 * 2 = 8$ total combinations.
List All Combinations: List out all possible combinations to ensure we have all eight. $\newline$ $1$ . White bread + Turkey + Swiss $\newline$ $2$ . White bread + Turkey + American $\newline$ $3$ . White bread + Ham + Swiss $\newline$ $4$ . White bread + Ham + American $\newline$ $5$ . Rye bread + Turkey + Swiss $\newline$ $6$ . Rye bread + Turkey + American $\newline$ $7$ . Rye bread + Ham + Swiss $\newline$ $8$ . Rye bread + Ham + American
Identify Subset: Identify the subset of sandwiches mentioned in the problem. $\newline$ The problem doesn't specify which sandwiches are in the subset, so we can't proceed without this information.

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