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 four Democrats.

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?

A box contains $25$ transistors $6$ of which are defective. If $6$ are selected at random, find the probability that

$$\textbf{a.}\hspace{10pt}\text{all are defective.}$$

$$\textbf{b.}\hspace{10pt}\text{none are defective.}$$

Evaluate the expression. Do not use a calculator.

$$P(7,7)$$

A coin is tossed three times. a) Draw a tree diagram to show all the possible outcomes. b) Use your tree diagram to calculate the probability of getting: i) three tails, ii) two heads, iii) no tails, iv) at least one tail.

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?

Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. Find the probability that a. Comic E will perform first. b. Comic C will perform fifth and comic B will perform last. c. The comedians will perform in the following order: D, E, C,A,B,F. d. Comic A or comic B will perform first.

Fill in each blank so that the resulting statement is true. Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. The probability that comic E will perform first is the number of ____ with comic E performing first divided by ____.

Fill in each blank so that the resulting statement is true. Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. The probability that comic E will perform first is the number of _____ with comic E performing first divided by ______.

Martha , Lee, Nancy, Paul , and Armando have all been invited to a dinner party. They arrive randomly and each person arrives at a different time. a. In how many ways can they arrive? b. In how many ways can Martha arrive first and Armando last? c. Find the probability that Martha will arrive first and Armando last.

Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.

$$\textbf{a.}\hspace{10pt}\text{In how many ways can they arrive?}$$

$$\textbf{b.}\hspace{10pt}\text{In how many ways can Martha arrive first and Armando last?}$$

$$\textbf{c.}\hspace{10pt}\text{Find the probability that Martha will arrive first and Armando last.}$$

Johanna, Dawn, Simone and Kelly run on a relay team. In a relay race, each runner takes a turn by running a leg that is an evenly divided portion of the total distance. Johanna, Dawn, Simone, and Kelly completed a 5-mile relay in 39 minutes. How far did each team member run? Write the answer as a mixed number and as a decimal.

Some three-digit numb ers, such as 101 and 313, read the same forward and backward . If you select a number from all three -digit numbers , find the probability that it will read the same forward and backward.

Some three-digit numbers, such as 101 and 313, read the same forward and backward. If you select a number from all three-digit numbers, find the possibility that it will read the same forward and backward.