A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?

Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?

If a child flips a coin five times in a row, what is the probability that she will receive at least one head and one tail?

In a certain group of 10 developers, 4 developers code only in Python and the rest program in either Ruby on Rails or PHP - but not both. If a developer organization is to choose a 3-member team, which must have at least 1 developer who codes in Python, how many different programming teams can be chosen?

A list of five integers has the following criteria: I. The median of the list is 6 II. The mode of the list is 2 III. The mean of the list is 5 Which of the following must true?

In a set of data, the average (arithmetic mean) equals the median. Which of the following must be true? I. The set consists of evenly spaced numbers. II. The set consists of an odd number of terms. III. The set has no mode.

A bag contains 3 green marbles, three red marbles and 2 blue marbles. If 3 marbles are randomly drawn from the bag, what is the probability of selecting 2 red marbles and 1 green marble?

The value of x is to be randomly selected from the integers from 1 to 10, inclusive, and then substituted into the equation y = x² - 4x + 3. What is the probability that the value of y will be negative?

There are 6 gentlemen and 5 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are seated together.

A set consists of 20 different numbers whose average is 10. Which of the following pairs, when added to the set of numbers, must reduce its standard deviation?

A bag contains 4 red, 4 green and 4 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?

In how many different ways can a soccer team finish the season with three wins, two losses, and one draw?

Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)

A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of colors in a pair does not matter)

Two children, one from each grade, will be chosen at random from 4 children from the 5th grade class and 4 children from the 4th grade class to win a prize. Each class has 3 eligible girls and one eligible boy. What is the probability that one boy and one girl will be chosen?

For each student in a certain class, a teacher adjusted the student’s test score using the formula y = 0.8x + 20, where x is the student’s original test score and y is the student’s adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class?

The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with (m + 2)?

All of the arrangements made in a flower shop yesterday contained roses, tulips, or lilies, or some combination of the three types. 32 of the arrangements made yesterday contained roses, 42 contained tulips, and 41 contained lilies. 16 of the arrangements made yesterday contained roses and tulips, 18 contained lilies and tulips, and 8 contained roses and lilies. If 5 of the arrangements made yesterday contained all three types, how many total arrangements were made?

There are 10 books on a shelf: 5 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?

In a certain accounting class of 90 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 65%, and the students on the make-up date had an average score of 85%, what was the average score for the entire class?

a, b, c, d, e In the list of different positive numbers above, the arithmetic mean is c. Which of the following changes to the list would necessarily increase the standard deviation?

In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?

If a choir consists of 5 boys and 6 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.

At a certain university, 7 students from the 10-student history department and 5 students from the 7-student English department will be selected to form a 12-student committee. At a neighboring university, 2 students from a 10-person math department and 3 students from a 7-student science department will be selected to form a 5-student focus group. What is the ratio of the number of ways in which the 12-student committee can be formed to the number of ways in which the 5-student focus group can be formed?

Three straight metal rods have an average (arithmetic mean) length of 77 inches and the shortest rod has a length of 65 inches. What is the maximum possible value of the median length, in inches, of the three rods?