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Quantity A

60!*20!

Quantity B

40!*30!


Quantity A

89!-88!-87!

Quantity B

$$ 88^{2}*87! $$


Five gift cards (one 100-dollar card, one 50-dollar card, one 25-dollar card and two 10-dollar card) have to be assigned to ten kids such that each kid receives no more than one card. In how many ways can these five cards be distributed?
A password is formed by 5 digits, including a "1", two "2" and two "4". How many different passwords can be formed?
What is the probability of selecting two socks of the same color when selecting two socks out of 5 pairs of different colors of socks (each pair of socks have the same color)?
Give your answer as a fraction.
What is the probability that A and B are both selected when you select 40 people out of a group of 100 (A and B included)?
Give your answer as a fraction.

Several 0 and 1 are arranged in a 10*10 palace as follows. Among all the number 0, what is the probability that they are arranged in both an odd row and an odd column?
Give your answer as a fraction.
When selecting two numbers without replacement from 5, 8, 9, 9, 9, what is the probability that the sum of the two selected numbers is a multiple of 3?
Give your answer as a fraction.
The probability that a component fails during first use is 0.1. If the component doesn`t fail during first use, then the probability that the component won`t fail in the following six months is 0.8

Quantity A

The probability that the component won`t fail within six months

Quantity B

0.75


In a box, the probability that the red ball is selected is $$\frac{5}{8}$$. Mark randomly selects balls twice from the box without replacement. If he didn`t get a red ball in the first attempt, then the probability that he gets a red ball in the second attempt is $$\frac{2}{3}$$. What is the probability that Mark get at least one red ball?
Give your answer as a fraction.
In seven continuous tosses, Event X or Event Y appears randomly each time. If Event X appear first, then the probability that Event X appears the next time is 0.3. If Event Y appears first, then the probability that Event Y appears the next time is 0.4. If Event X appears in the fifth time, then what is the probability that Event X appears in the seventh time?
Give your answer as a decimal.
0 < a < b < 1

c and d are positive integers such that c < d

Quantity A

$$a^{c-d}$$

Quantity B

$$b^{d-c}$$


In 1998, how many of the imported towels were not imported from China?
If the average (arithmetic mean) number of towels imported from China per month was the same for the last 3 months of 2000 as it was for the first 9 months of 2000, approximately how many million dozen towels were imported from China during the 12 months of 2000?
In 1999, the ratio of the number of towels imported from China to the total number of towels imported from countries other than China was closets to which of the following?
For each value x in a list of values with mean m, the absolute deviation of x from the mean is defined as |x-m|.

A certain online course is offered once a month at a university. The number of people who register for the course each month is at least 5 and at most 30. For the past 6 months, the mean number of people who registered for the course per month was 20. For the numbers of people who registered for the course monthly for the past 6 months, which of the following values could be the sum of the absolute deviations from the mean?

Indicate all such values.
A certain truck takes 10 trips to transport 2,000 cartons from warehouse A to warehouse B. For each trip except the 10th trip, the truck is loaded to its full carrying capacity of x cartons. On the 10th trip, the truck is loaded with the remaining cartons.

Quantity A

x

Quantity B

210


Dr. Bradley treated a different number of patients on each of the 5 working days last week, and the least number of patients treated on any of the days was 20. No patient was treated on more than one day.

Quantity A

The least possible total number of patients that Dr. Bradley treated on the 5 working days last week

Quantity B

110


$$a_1$$ , $$a_2$$ , $$a_3$$ , ...... , $$a_{99}$$

In the sequence shown, each term after the first is 1 greater than the preceding term. If the sum of all the 99 terms of the sequence is 99, then what is the value of the first term of the sequence?

Quantity A

The number of odd integers between $$\sqrt{12}$$ and $$12^{2}$$

Quantity B

70


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