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Signal Flags How many different flag signals, each consisting of 7 flags hung vertically, can be made when there are 3 indistinguishable red flags, 2 blue flags, and 2 white flags?

Word Permutations How many permutations can be made using all the letters in the word MASSACHUSETTS?

Building a New Home In building new homes, a contractor finds that the probability of a home buyer selecting a two-car garage is 0.70 and of selecting a one-car garage is 0.20. Find the probability that the buyer will select no garage. The builder does not build houses with three-car or more garages.

Computers in Elementary Schools Elementary and secondary schools were classified by the number of computers they had. $$ \begin{array}{l|llllll}{\text { Computers }} & {1-10} & {11-20} & {21-50} & {51-100} & {100+} \\ \hline \text { Schools } & {3170} & {4590} & {16,741} & {23,753} & {34,803}\end{array} $$ Choose one school at random. Find the probability that it has a. 50 or fewer computers b. More than 100 computers c. No more than 20 computers

Congressional Terms Below is given the summary from the 112 th Congress of Senators whose terms end in \(2013,2015,\) or 2017 . $$ \begin{array}{cccc}{} & {2013} & {2015} & {2017} \\ \hline \text { Democrat } & {21} & {20} & {1} \\ {\text { Republican }} & {8} & {15} & {13}\end{array} $$ Choose one of these Senators at random and find $$ \begin{array}{l}{\text { a. } P(\text { Democrat and term expires in } 2015\text { ) } } \\ {\text { b. } P(\text { Republican or term expires in } 2013)} \\ {\text { c. } P(\text { Republican given term expires in } 2017)}\end{array} $$ Are the events 鈥淩epublican鈥� and 鈥渢erm expires in 2015鈥� independent? Explain.

College Debt The following information shows the amount of debt students who graduated from college incur for a specific year. $$ \begin{array}{cccc}{\$ 1 \text { to }} & {\$ 5001 \text { to }} & {\$ 20,001 \text { to }} & {} \\ {\$ 5000} & {\$ 20,000} & {\$ 50,000} & {\$ 50,000+} \\\ {27 \%} & {40 \%} & {19 \%} & {14 \%}\end{array} $$ If a person who graduates has some debt, find the probability that $$ \begin{array}{l}{\text { a. It is less than } \$ 5001} \\ {\text { b. It is more than } \$ 20,000} \\ {\text { c. It is between } \$ 1 \text { and } \$ 20,000} \\ {\text { d. It is more than } \$ 50,000}\end{array} $$

Pizza and Salads In a pizza restaurant, \(95 \%\) of the customers order pizza. If \(65 \%\) of the customers order pizza and a salad, find the probability that a customer who orders pizza will also order a salad.

Toothpaste Display How many different ways can 5 identical tubes of tartar control toothpaste, 3 identical tubes of bright white toothpaste, and 4 identical tubes of mint toothpaste be arranged in a grocery store counter display?

Suppose that \(P(A)=0.42, P(B)=0.38\), and \(P(A \text { or } B)=0.70 .\) Are \(A\) and \(B\) mutually exclusive? Explain.

Population of Hawaii The population of Hawaii is \(22.7 \%\) white, \(1.5 \%\) African-American, \(37.7 \%\) Asian, \(0.2 \%\) Native American/Alaskan, \(9.46 \%\) Native Hawaiian/Pacific Islander, \(8.9 \%\) Hispanic, \(19.4 \%\) two or more races, and \(0.14 \%\) some other. Choose one Hawaiian resident at random. What is the probability that he/she is a Native Hawaiian or Pacific Islander? Asian? White?