#### 题目列表

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?

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?

S is the set of all ordered pairs (x, y) of integers such that -10 ≤ x ≤ 10 and -5 ≤ y ≤ 15.

#### Quantity A

The number of ordered pairs (x, y) in S such that x=y

16

#### Quantity A

The number of ordered triples ($x_1$, $x_2$, $x_3$), where $x_1$, $x_2$ and $x_3$ are non-negative integers such that $x_1$+$x_2$+$x_3$=9

#### Quantity B

55

In how many ways can 5 identical apples be put into 3 different bowls such that at least 1 apple is included in each bowl?
Freds suitcase contains 4 shirts, 3 pair of pants, and 2 pair of shoes. A matching outfit consists of any shirts, any pair of pants, and a pair of shoes, except that one of the shirts does not match one of the pairs of pants. How many matching outfits can be selected from Freds suitcase?
One person has 5 shirts, 4 trousers and 3 shoes, of which one shirt and one trousers can not be combined. How many combinations are possible?
Four guests A, B, C and D have to be assigned into three different office rooms (one double room and two single rooms) such that A and B won`t have to stay in the double room at the same time. How many ways in total can they be assigned into these office rooms?
How many different 5-digit numbers can be formed by one "1",two "2",and two "3"?
The letters in a certain name can be arranged in exactly 180 different orders. Which of the following could be that name?
The vehicles of Company W are numbered consecutively from 1 to 650. The vehicles with a number that ends with one of the digits 1, 2, 3, 4, or 5 are used by Division A. Vehicles with a number between 130 and 389, inclusive, are trucks. If a company vehicle is chosen at random, what is the probability that the chosen vehicle will be a truck used by Division 1?
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?

When randomly selecting four different integers from 1 to 9, inclusive, the probability that 1, 2, 3 and 4 are selected in the above order is x, while the probability that 1,2 3 and 4 are selected no matter in what order is y. What is the ratio of x to y?

Even A and B are complementary events. The probability that event A occurs is p, while the probability that event B occurs is 2p

p

#### Quantity B

1-p

p is a value of probability greater than 0.5

2p

#### Quantity B

$p^{2}$

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