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题目内容
n is a positive even integer.

Quantity A

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

Quantity B

$$(2)(\frac{n}{2})!$$
A password is formed by 5 different letters (A, B, C, D, E), if no letter can be repeated in one password, how many different passwords can be formed?
How many 5-digit odd integers can be formed out of 3, 4, 6, 7, 9 such that each number is used for only once?
A father purchased theater tickets for 6 adjacent seats in the same row of seats for himself, his wife, and their 4 children. How many seating arrangements are possible if the father and mother sit in the 2 middle seats?
There are three different frames and five different pictures. Now choose three pictures to put into frames, one for each frame, how many possible ways to put them.
A students selects books for reading material randomly,and which of the following has exactly 10 different ways of selection?
Indicate all such statements.
S={1, 3, 5, 7,.............,397, 399}

Set S consists of the odd numbers from 1 to 399, inclusive. How many different ordered pairs $$(p, t)$$ can be formed, where $$p$$ and $$t$$ are numbers in S and $$p \lt t$$?

(Note: The sum of the integers from $$1$$ to $$n$$, inclusive, is given by the formula $$\frac{n(n+1)}{2}$$ for all positive integers $$n$$.)
There are four people, S, M, K and R. Some people should be selected from these four people to form a committee. The committee is required to have at least two people. How many different methods are there in total?
How many points (r, s) can be formed so that r < s, and that the x and y-coordinates of the point are both selected from odd integers between 1 and 399, inclusive?
Two boys and two girls are selected from six boys and four girls. How many methods are there?
In how many different ways can 5 identical small balls be placed in 3 different baskets so that each basket must have at least one small ball?
There are four books A, B, C, and D, how many arrangements if A and B must be next to each other?
A, B, C, D and E need to take seats such that A and B sit next to each other. How many ways can they arrange the seats?
Four different books A, B, C, D are to be placed on the shelf, A and B must be put together. How many different ways can the four books be placed?
Four different toys need to be put into three different kids. At least one toy should be given to each kid. In how many ways can these toys be arranged?
If there are 6,840 different ways when promoting 3 out of 20 employees for three different positions, then in how many ways can 3 employees be selected out of 20 for three identical positions?
How many different 5-digit numbers can be formed by one "1",two "2",and two "5"?
The 8 items A, B, C, D, E, F, G, and H are to be displayed on a straight line. In how many ways can the items be displayed if item B must be placed in any position that is to the right of item A,and item C must be placed in any position that is to the right of B?
Someone rearranges all the letters from the word "Mississippi"

Quantity A

The probability that all the same vowel letters are arranged together

Quantity B

The probability that all the same consonant letters are arranged together
There are 20 students in class with 10 girls and 10 boys. A teacher randomly selects some students and the first 6 students are all girls.

Quantity A

The probability that the 7th student is a girl

Quantity B

$$\frac{2}{7}$$

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