## Related questions with answers

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

VerifiedIn 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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