A committee of four Congressmen will be selected from a group of seven Democrats and three Republicans. Find the number of ways of obtaining exactly three Democrats.

Nine people are to be distributed among three committees of two, three, and four members, and a chairperson is to be selected for each committee. How many ways can this be done? (Hint: Break the task into the following sequence of parts.) (a) Select the members of the two-person comm ittee. (b) Select the members of the three-person comm ittee. (c) Select the chair of the two-person committee. (d) Select the chair of the three-person committee. (e) Select the chair of the four-person committee.

Diana Baniak, searching for an Ecology class, knows that it must be in one of nine classrooms. Since the professor does not allow people to enter after the class has begun, and there is very little time left, she decides to try just four of the rooms at random. How many of the selections from the previous exercise will fail to locate the class?

Sheryl Jett wants to name her new baby so that his monogram (first, middle, and last initials) will be distinct letters in alphabetical order and he will share her last name. How many different monograms could she select?

For each situation, (a) write an equation in the form y=mx+b, (b) find and interpret the ordered pair associated with the equation for x=5, and (c) answer the question. There is a $30 fee to rent a chain saw plus$6 per day. Let x represent the number of days the saw is rented and y represent the charge to the user in dollars. If the total charge is $138, for how many days is the saw rented?

Evaluate ${} _{12} \mathrm{P}_3$.

If you roll two fair dice (say red and green), in how many ways can you obtain a different number on each die?

This exercise concerns 5-card poker hands from a standard 52-card deck. How many hands contain a royal straight flush (that is, the 10, jack, queen, king, ace of one suit)?

A royal flush consists of an ace, king, queen, jack, and 10 all in the same suit. If 7 cards are dealt at random from a standard deck of 52 cards, determine the probability of getting a (a) Royal flush in spades. (b) Royal flush in any suit.

Solve the given problem.

A frog leaps from a stump three feet high and lands four feet from the base of the stump. We can consider the initial position of the frog to be at $(0,3)$ and its landing position to be at $(4,0)$.

It is determined that the height $h$ in feet of the frog as a function of its distance $x$ from the base of the stump is given by

$$h(x)=-0.5 x^2+1.25 x+3 .$$

(a) How high was the frog when its horizontal distance $x$ from the base of the stump was $2$ feet?

(b) What was the horizontal distance from the base of the stump when the frog was $3.25$ feet above the ground?

(c) At what horizontal distance from the base of the stump did the frog reach its highest point?

(d) What was the maximum height reached by the frog?

Of the $36$ possibilities, determine the number for which the sum for rolling two dice is $3$.

The trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in their proper order. If there are seven entries in the trifecta race, how many tickets must you purchase to guarantee a win?

In a state lottery, you must correctly select 5 numbers (in any order) out of 40 to win the top prize. (a) How many ways can 5 numbers be chosen from 40 numbers? (b) You purchase one lottery ticket. What is the probability that you will win the top prize?

In how many ways can we select a chairperson, vice-chairperson, secretary, and treasurer from a group of 12 persons?