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Question

# A restaurant has 8 different appetizers on the menu, as shown in the table. They also offer an appetizer sampler, which contains any 3 of the appetizers served on a single plate. How many different appetizer samplers can be created? The order in which the appetizers are selected does not matter. Appetizers Nachos Chicken Wings Chicken Quesadilla Vegetarian Egg Rolls Potato Skins Soft Pretzels Beef Chili Guacamole Dip (A) Find the number appetizer samplers that are possible if the order of selection does matter . This is the number of permutations of 8 objects taken 3 at a time.${ }_8 P_3=\frac{?}{\left({?}-{?}\right)!}=\frac{?}{?}=?$(B) Find the number of different ways to select a particular group of appetizers. This is the number of permutations of 3 objects.${ }_3 P_3=\frac{?}{\left({?}-{?}\right)!}=\frac{?}{?}=?$(C) To find the number of possible appetizer samplers if the order of selection does not matter, divide the answer to part $\mathrm{A}$ by the answer to part $\mathrm{B}$.So the number of appetizer samplers that can be created is $\frac{?}{?}=?$.Explain why the answer to Part A was divided by the answer to Part B.

Solution

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In the exercise, we can notice that the answer of Part A is the total number of appetizers samplers that can be created taking three of them from a total of eight available, being this our sample space $n(S)=_{8}\text{P}_{3}$.

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