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题目内容
Three numbers are to be selected at random and without replacement from the five numbers 4, 5, 7, 8 and 11. What is the probability that the three numbers selected could be the lengths of the sides of a triangle?
What is the probability that the one 3-digit and one 2-digit integers that could be formed out of 1, 2, 3, 4 and 5 (each figure is used for only once) are both even integers?

Give your answer as a fraction.
The units digit of $$7^{n}$$ is r, and the units digit of $$9^{n}$$ is t, where n, r, and t are positive integers. Which of the following could be the value of r+t?

Indicate all such values.
How many positive integers less than or equal to 603 are multiples of 2 or multiples of 3 or both?
How many integers between 100 and 1,000 are multiples of 7?
The sum of three different positive integers is 11.

Which two of the following statements together provide sufficient information to determine the three integers?

Indicate two such statements.
Z=$$123^{4}$$-$$123^{3}$$+$$123^{2}$$-123

What is the remainder when Z is divided by 122?
For 7 soccer ball teams, each of them has to play with all the other teams. However, to decide which team wins, every two teams have to play 3 rounds and the team that win for the most times will ultimately win. How many rounds of game do all teams have to play in total?
n is a positive integer.

Quantity A

$$\frac{1}{3^{n}}$$

Quantity B

$$3(\frac{1}{4^{n}})$$
How many positive divisors of 210 can be expressed as a product of two prime factors?
xy ≠ 0 , x > y

Quantity A

$$\frac{1}{x}$$

Quantity B

$$\frac{1}{y}$$
a ≠ 0

Quantity A

a+1

Quantity B

$$\frac{1}{a}$$ - 1
-1 < x < 1

Quantity A

|1-x|

Quantity B

1

Quantity A

The number of positive even integers less than 100, each of which is the square of an integer

Quantity B

The number of positive odd integers less than 100, each of which is the square of an integer
There are two parallel lines, and the third line intersects these two lines.

Quantity A

The number of points with equal distance from three lines

Quantity B

3
Two sides of an isosceles triangle have lengths 5 and 5.

Quantity A

The perimeter of the triangle

Quantity B

15
Eight students of different heights need to be arranged into two rows of seats. Each row has four seats. For each column, the student in the row ahead needs to be shorter than the student in the row behind. In how many ways can these students be arranged?
An urn contains 4 red balls, 8 green balls and 2 yellow balls. Five balls are randomly selected WITH replacement from the urn. What is the probability that 1 red ball, 2 green balls, and 2 yellow balls will be selected?

Give your answer as a fraction.
An eight-digit integer is formed by three "1" and five "2". How many different such integers can be formed?

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