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.

the sample spaces are large and you should use the counting principles The deck for a card game is made up of 108 cards. Twenty-five each are red, yellow, blue, and green, and eight are wild cards. Each player is randomly dealt a seven-card hand. What is the probability that a hand will contain exactly two wild cards?

Find the probability.

The probability of flipping a coin and getting a heads, given that the probability of getting a tails is the same, and there is no chance that the coin lands on its side;

Find the probability.

The probability of flipping a coin and getting a heads, given that the probability of getting a tails is the same, and there is no chance that the coin lands on its side.

A bag contains 3 blue marbles, 5 red marbles, and 4 green marbles. You choose one without looking. What is the probability that it is red or green?

How would you describe mutually exclusive events to another student in your own words? How could you use a Venn diagram to assist in your explanation?

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A={3, 5, 7, 8}, B={2, 3, 8, 9, 10}, and C={1, 4, 7, 8}. Use the roster method to write each of the following sets.

$$A \cap \left( B ^ { \prime } \cup C \right)$$

Use the sets below to find the indicated set for the following problem.

U= {1,2,3,4,5,6,7,8,9}

A= {1,3,5,7,9}

B= {2,4,6,8}

C= {1,2,4,5,7,9}

$$A \cup C$$

Set A is the set of factors of 12, set B is the set of even natural numbers less than 13, set C is the set of odd natural numbers less than 13, and set D is the set of even natural numbers less than 7. The universal set for these questions is the set of natural numbers less than 13.

So, $A=\{1,2,3,4,6,12\}, B=\{2,4,6,8,10,12\}$,

$C=\{1,3,5,7,9,11\}, D=\{2,4,6\}$, and

$$U=\{1,2,3,4,5,6,7,8,9,10,11,12\}$$

Answer the following question.

Is $D \subset A$ ? Explain why or why not.

Do sets always have an intersection that is not the empty set? Provide an example to support your conclusion.

An MP3 player has a playlist with 12 songs. You select the shuffle option, which plays each song in a random order without repetition, for the playlist. In how many different orders can the songs be played?

Jonah is arranging books on a shelf. The order of the books matters to him. There are 336 ways he can arrange the books. Write Yes or No for A-C.

A. He might be arranging 3 books from a selection of 8 different books.

B. He might be arranging 4 books from a selection of 8 different books.

C. He might be arranging 5 books from a selection of 8 different books.

How well do you think President Kennedy handled the Cuban missile crisis? Justify your opinion with specific examples from the text.

Use the simple interest formula method.

Harry Taylor plans to pay an ordinary annuity of $\$ 5,000$ annually for ten years. The annual rate of interest is $3.8 \%$. How much will Harry have at the end of three years? How much interest will he earn on the investment after three years?