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题目内容
How many different five-digit positive integers can be formed in which each of the digits 1, 2, 3, 6, and 7 is used exactly once?
A product testing company will test 7 different fax machines by linking every possible pair and transmitting first from one machine to the other and then transmitting in the opposite direction. Thus, 2 transmissions will occur in testing each pair. If each transmission takes 10 minutes, how many minutes of transmission time will it take to test all of the machines?
How many different four-digit integers contain each of the four digits 3, 4, 5, and 6 exactly once?
Of the 12 members of a certain club, one is to be selected to serve as president, and another is to be selected to serve as secretary. How many different choices of president and secretary can be selected from the 12 members of the club?
Six students are competing in a contest that will result in a list of three winners:one first-place winner, one second-place winner, and one third-place winner. How many different lists of three winners are possible?
On a certain farm, the same set of 5 different chores is to be completed each day, but the order in which the chores are completed changes from day to day.The integer x represents the greatest possible number of consecutive days that can occur before an ordering of the chores must be repeated.

Quantity A

x

Quantity B

100
How many different combinations of 5 cards can be chosen from a pack of 52 cards?

Quantity A

The number of different groups of 2 kittens that can be chosen from a litter of 8 kittens

Quantity B

The number of different groups of 6 puppies that can be chosen from a litter of 8 puppies
In a certain corporation,an employee council will consist of 3 employees who will be selected from 20 eligible employees. If each of the 3 positions on the council has a different role on the council,then there are 6,840 possible 3-employee selections from the 20 eligible employees. How many possible 3-employee selections are there if the 3 positions all have the same role?
A dinner menu offers 8 different entrees and 6 different vegetables. How many different combinations of 1 entrée and 2 different vegetables are possible?
In a group of 10 people, exactly 4 are vegetarians. A committee of 3 will be formed by randomly selecting 3 people from the group. How many of the possible 3-member committees would include exactly 2 vegetarian members?
A 3-member panel is to be selected from a group of 5 women and 3 men. If the panel is to be composed of 2 women and 1 man, how many different 3-member panels are possible?


The table lists the prices of all types of donuts available at Donut Shop J. How many different combinations of two donuts of different types can be purchased at Donut Shop J if the total of the prices of the two donuts must be less than $1.00?
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?

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