How do you determine whether choosing a group of objects involves permutations?

Jane has 16 cards. Ten of the cards look exactly the same and have the number 1 on them. The other 6 cards look exactly the same and have the number 2 on them. Jane is going to make a row containing all 16 cards. How many different ways can she order the row?

Answer the following question.

Can a subset of A contain elements of $A^{C \text { ? }}$ Why or why not?

How do you determine whether choosing a group of objects involves combinations?

It was observed that there are 6 permutations of the letters A, B, and C. They are ABC, ACB, BAC, CAB, and CBA. If the conditions are changed so that the order of selection does not matter, what happens to these 6 different groups?

The table shows the data for car insurance quotes for 125 drivers made by an insurance company in one week.

$$\begin{array}{|l|c|c|c|} \hline {} & \text { Teen } & \text { Adult (20 or over) } & \text { Total } \\ \hline \mathbf{0} \text { accidents } & 15 & 53 & 68 \\ \hline \mathbf{1} \text { accident } & 4 & 32 & 36 \\ \hline \mathbf{2}+\text { accidents } & 9 & 12 & 21 \\ \hline \text { Total } & 28 & 97 & 125 \\ \hline \end{array}$$

You randomly choose one of the drivers. Find the probability of the following event.

The driver is a teen or a driver with $2+$ accidents.

Determine if the given event are mutually exclusive. If not, explain why.

Rolling an even number or a prime number on a number cube

You have a set of 10 cards numbered 1 to 10. You choose a card at random. Event A is choosing a number less than 7. Event B is choosing an odd number. Calculate the probability.

$P(B)$

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;

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}

$$A \cup C$$

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.

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.

(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.

Answer the following question.

A cat has a litter of 6 kittens. You plan to adopt 2 of the kittens. In how many ways can you choose 2 of the kittens from the litter?

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.