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At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
If an integer is chosen at random from the integers between 3,000 and 3,799,inclusive,what is the probability that the chosen integer will be between 3,020 and 3,039, inclusive?
A number is to be selected at random from the integers from 100 through 999.

Quantity A

The probability that exactly two adjacent digits of the number selected will be the same

Quantity B

$$\frac{1}{5}$$
At a research organization, a committee consists of 3 members from department A, 3 members from department B, and 3 members from department C. From the committee, 2 different members will be selected at random to attend a conference. What is the probability that both of the members selected will be from department C?
A certain group of 10 people consists of 5 men and 5 women. From this group, 2 people are to be selected at random. The probability that the 2 people selected will consist of 1 man and 1 woman is equal to p.

Quantity A

p

Quantity B

$$\frac{1}{2}$$
Of the 7 guests at a party, 3 are close friends of the host and 4 are acquaintances of the host. At the end of the party,the host will randomly select 2 different guests to win prizes. What is the probability that both of the prizewinners will be among the 3 close friends of the host?
Two different integers, x and y, are to be selected at random from the set of positive integers less than 100.

Quantity A

The probability that both x and y will be even

Quantity B

The probability that x+y will be even
S={0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

A two-member subset {k, m} of the set S shown above is to be selected at random. What is the probability that the members of the subset will satisfy the equation |k – m| = 2?
If a four-digit number is to be formed from the digits 1, 2, 3, and 4 by selecting each digit at random and using each digit only once, what is the probability that the number formed will be greater than 3,000?
For all bookstores in 1996, approximately what was the average (arithmetic mean) book sales per store?
In 1996, companies G, H, and K owned a total of 110 bookstores. If beginning in the first half of 1997, these three companies were to purchase a total of 15 of the remaining 1996 bookstores every half year, what is the first year in which all of the 1996 bookstores would be owned by these three companies?
If the total annual booksales in 1992 was $50.0 million and if this total increased by at least $1.0 million annually from 1992 to 1996, what was the greatest possible annual increase in this total from 1992 to 1996?
$$k > 0$$

Quantity A

The volume of a hemisphere (half of a sphere) that has radius $$k$$

Quantity B

The volume of a right circular cylinder that has height $$k$$ and whose base has radius $$k$$
Three 16-ounce bottles, M, R,and S, are filled with three different beverages. The amount of sugar contained in bottle M is $$\frac{1}{4}$$ of the amount of sugar contained in bottle R and is $$\frac{2}{5}$$ of the amount of sugar contained in bottle S. The amount of sugar contained in bottles R and S combined is what fraction of the amount of sugar contained in bottle R?
n is an integer and $$(n-5)^{9-n}=1$$.

Quantity A

n

Quantity B

4
A monument is constructed on level ground in the shape of a pyramid with a square base. If each edge of the monument is 10 meters long, how many meters above the ground is the tip of the monument?
What fraction is equivalent to the repeating decimal $$0.2\grave{7}$$ (7 being repeated)?
A certain distribution of 6 temperatures $$t_1$$, $$t_2$$, $$t_3$$, $$t_4$$, $$t_5$$, $$t_6$$ has a standard deviation of 2.14 degrees Celsius. Which of the following distributions of temperatures must also have a standard deviation of 2.14 degrees Celsius?

Indicate all such distributions.

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