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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?

Give your answer as a fraction.
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 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 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?
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?

Give your answer as a fraction.
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?

Give your answer as a fraction.
Even A and B are complementary events. The probability that event A occurs is p, while the probability that event B occurs is 2p

Quantity A

p

Quantity B

1-p


p is a value of probability greater than 0.5

Quantity A

2p

Quantity B

$$p^{2}$$


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