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题目内容
Among all the 24 different positive four-digit integers formed out of 6, 7, 8, 9, at which place will 8697 rank from the least to the greatest?
An artist has 3 hooks on the wall and 5 different pictures. How many different arrangements of 3 pictures can be formed if the artist puts one of the 5 pictures on each hook?

Quantity A

$$\frac{100!}{99!}$$

Quantity B

$$\frac{ (100!-99!)}{98!}$$

Quantity A

$$\frac{(5!+6!)}{(6!+7!)}$$

Quantity B

$$\frac{1}{6}$$

Quantity A

20!+19!+18!

Quantity B

400(18!)


Quantity A

$$\frac{23!}{(11!*13!)}$$

Quantity B

$$\frac{23!}{(10!*14!)}$$
$$n$$ is an even integer greater than $$2$$.

Quantity A

$$\frac{n!}{(\frac{n}{2})!}$$

Quantity B

2($$\frac{n}{2}$$)!
If 3 integers are randomly selected out of 1, 2, 3, 4, 5 (no repeated numbers are allowed) to form a positive three-digit integer, then how many different integers can be formed?
In a kindergarten, three shorter kids sit in the first row, while four taller ones sit in the second row. In how many ways can they be arranged?
How many 6-digit integers greater than 321,000 can be formed such that each of the digits 1, 2, 3, 4, 5, and 6 is used once in each 6-digit integer?
The 9 computers in an office are to be interconnected by cables so that each computer is connected directly to each of the other computers. If each cable that connects a pair of the computers counts as one cable, how many cables are needed?
In a university, a certain committee consists of 6 faculty members, 4 administrators and 3 students. A subcommittee of 5 members will be selected from the committee. Professor Smith, who is one of the 6 faculty members, and Ms. Wilson, who is one of the 4 administrators must be on the subcommittee. The other 3 subcommittee members will be selected at random from the rest of the committee. How many different 5-member subcommittees can be selected?
Set K consists of 9 positive integers, 5 of which are prime numbers. How many subsets of K consist of 3 integers such that 2 integers are prime numbers and 1 integer is not a prime number?
How many different words that start with "mrt" can you get if you rearrange the letters of the word "merit"?
x and y are both positive integers, and 1 ≤ y ≤ 8, x < y, how many (x, y) coordinates are there?
Set A={12, 13, 14, 15, 16}

Set B={13, 14, 15, 16, 17}

How many different sums can be formed when selecting one number from each set and added together?


The figure above represents a game board with a chip at staring point M. On successive plays, the chip may be moved along the lines from one labled point to an adjacent labled point, but may not be moved to the same point twice. Along how many different paths can the chip be moved from M to N in this game?


If Mark randomly walks from point P to point R (he can only walk either rightward or upward), what is the probability that he passes through point Q?

Give your answer as a fraction.
Ordered pairs (x, y), where1 ≤ y < x ≤ 8, x and y are both integers

How many different pairs are there?
A number is to be randomly selected from the integers from 1 through 87.

Quantity A

The probability that the number selected will have a units digit of 6

Quantity B

The probability that the number selected will have a tens digit of 6

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