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题目内容
How many three-digit numbers could be formed out of 2, 7 and 5 such that at least one figure is used for at least twice?
There are 5!, or 120, ways of arranging 5 different solid-colored flags side by side. If the colors of the flags are red, blue, yellow, green, and orange, how many of those arrangements have either the red flag or the blue flag in the middle position?


In how many ways can letter a b and c be assigned into a nine palace such that no letter is used more than once in each column and each row?
In how many more ways can you select 4 books out of 8 books than when you select 4 books out of 6 books?
How many different products can be formed when selecting 2 different numbers from 0, 2, 6, 8 and 12 and multiplying them together?
In how many ways can you select one Product A and two Product B out of 8 types of Product A and 6 types of Product B?
The budget of 5 countries are 0.7 billion, 1.3 billion, 1.7 billion, 2.7 billion and 3.2 billion, respectively. In how many ways can you select 3 countries from all the countries such that the total budget of these 3 countries is over 4 billion?
40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. In how many ways can these DVDs be arranged?
Among 50 spare parts. 2 are broken. What is the probability that both are broken when you select two spare parts from the total?
Give your answer as a fraction.
What is the ratio of a two-digit integer whose tens digit can be divisible by 2 to all the two-digit integers?
Give your answer as a fraction.
The total number of product A and B in a box is 20. The unit price of A and B is 0.2 and 0.4, respectively, and the total price of them is 5.6. What is the probability that someone randomly selects a product from the box and selects product A?
Give your answer as a fraction.
If one number is chosen at random from the first 1,000 positive integers, what is the probability that the number chosen has at least one digit with the number 6?
Give your answer as a fraction.
5 balls are in a box, including 1 red ball and 4 green balls. Of a volunteer picks up 2 balls randomly from the box, what is the probability that both balls are green?
Give your answer as a fraction.
Among 30 jackets, 10 are red, 10 are black and 10 are yellow. When selecting 5 out of these 30 jackets, what is the probability that 3 red jackets, 1 black jackets and 1 yellow jackets are selected?
Give your answer as a fraction.
Set R={-3, -2, -1, 0, 1, 2, 3}
Set T={-7, -6, -5, -4, -3, -2}
If an integer is to be randomly selected from set S and an integer is to be randomly selected from set R, what is the probability that the product of the two integers selected will be positive?
Give your answer as a fraction.
From a class of 8 students, of which 5 students are female, a president and a vice president are to be chosen at random. If a student cannot be both the president and the vice president, what is the probability that the president and the vice president will both be female?
Give your answer as a fraction.
Each digit of a 3-digit integer is a positive integer that is divisible by 3. What is the probability that the tens digit of such integers is an odd number and the hundreds digit of the integer is an even number?
Give your answer as a fraction.
The probability that a person will succeed at a particular task is p.

Quantity A

p(1-p)

Quantity B

0.4
Probability XX of Event A means the ratio of the probability that Event A occurs to the probability that Event A does not occur. If Probability XX of getting heads when tossing a coin is $$\frac{3}{7}$$, then what is the probability of getting heads when tossing the coin?
Give your answer as a fraction.
A and B are mutually independent and the probability that Event A occurs is the same as that of the probability that Event B occurs (both equals to 0.3).

Quantity A

The probability that Event A occurs when Event B does not occur

Quantity B

0.3

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