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In how many ways can five children posing for a photograph line up in a row?

Drawing Marbles Find the probability for the experiment of drawing two marbles at random (without replacement) from a bag containing one green, two yellow, and three red marbles. Neither marble is yellow.

Data Analysis An independent polling organization interviews one hundred college students to determine their political party affiliations and whether they favor a balanced-budget amendment to the Constitution. The table lists the results of the study. In the table, \(D\) represents Democrat and \(R\) represents Republican. $$\begin{array}{|l|c|c|c|c|} \hline & \text { Favor } & \text { Not Favor } & \text { Unsure } & \text { Total } \\ \hline D & 23 & 25 & 7 & 55 \\ \hline R & 32 & 9 & 4 & 45 \\ \hline \text { Total } & 55 & 34 & 11 & 100 \\ \hline \end{array}$$ Find the probability that a person selected at random from the sample is as described. (a) A person who does not favor the amendment (b) A Republican (c) A Democrat who favors the amendment

Education In a high school graduating class of 128 students, 52 are on the honor roll. Of these, 48 are going on to college; of the other 76 students, 56 are going on to college. What is the probability that a student selected at random from the class is (a) going to college, (b) not going to college, and (c) not going to college and on the honor roll?

Write an expression for the \(n\) th term of the geometric sequence. Then find the indicated term. $$a_{1}=1000, r=1.005, n=60$$

Winning an Election Three people are running for president of a class. The results of a poll indicate that the first candidate has an estimated \(37 \%\) chance of winning and the second candidate has an estimated \(44 \%\) chance of winning. What is the probability that the third candidate will win?

Eight sprinters have qualified for the finals in the 100 -meter dash at the NCAA national track meet. In how many ways can the sprinters come in first, second, and third? (Assume there are no ties.)

Use mathematical induction to find a formula for the sum of the first \(n\) terms of the sequence. $$3,-\frac{9}{2}, \frac{27}{4},-\frac{81}{8}, \dots$$

On a game show, you are given five digits to arrange in the proper order to form the price of a car. If you are correct, then you win the car. What is the probability of winning, given the following conditions? (a) You guess the position of each digit. (b) You know the first digit and guess the positions of the other digits.

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. (a) What is the probability that a hand will contain exactly two wild cards? (b) What is the probability that a hand will contain two wild cards, two red cards, and three blue cards?