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题目内容
The 9 computers in an office are to be interconnected by cables so that each computer is connected directly to each of the other computers. If each cable that connects a pair of the computers counts as one cable, how many cables are needed?
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?


The figure above represents a game board with a chip at staring point M. On successive plays, the chip may be moved along the lines from one labled point to an adjacent labled point, but may not be moved to the same point twice. Along how many different paths can the chip be moved from M to N in this game?


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?

Give your answer as a fraction.
Ordered pairs (x, y), where1 ≤ y < x ≤ 8, x and y are both integers

How many different pairs are there?
A number is to be randomly selected from the integers from 1 through 87.

Quantity A

The probability that the number selected will have a units digit of 6

Quantity B

The probability that the number selected will have a tens digit of 6
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

Quantity B

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?
Fred`s 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 any 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 Fred`s 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?


Several 0 and 1 are arranged in a 10*10 palace as follows. Among all the number 0, what is the probability that the selected 0 is located where the number of 0 in that row is odd while the number of 0 in that column is also odd?

Give your answer as a fraction.
In a box of red, blue and green balls, if the ratio of red to blue is 2:3, the ratio of blue to green is 4:3, then what ratio of all balls in the box are blue ones?

Give your answer as a fraction.

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