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Question 1: (1 point)
When two fair dice are rolled, there are 36 possible outcomes.
How many possible outcomes would there be if six fair dice were rolled?
There would be ____________ possible outcomes.
Question 2: (1 point)
Evaluate the following expressions:
a)
10P6
The answer is ____________
(Type an integer or a simplified fraction)
b)
16C7
The answer is ____________
(Type an integer or a simplified fraction)
c)
10!(10 − 6)!
The answer is ____________
(Type an integer or a simplified fraction)
d)
16!7!(16−7)!
The answer is ____________
(Type an integer or a simplified fraction)
Question 3: (1 point)
A multiple-choice test consists of 6 questions with each question having 5 possible answers.
How many different ways are there to mark the answers?
There are ____________ ways.
Question 4: (1 point)
5 (fair, 6-sided) dice are rolled simultaneously.
Determine the number of possible outcomes in which at least one of the die shows 6?
Question 5: (1 point)
In how many ways could members of the following club line up all 7 members for a photograph?
N = [Tom, Mick, Bob, Donald, Monica, Nik, Alice]
The number of ways is: ____________
Question 6: (1 point)
Consider the numbers {7,4,3,8,17}.
In how many ways can I order these numbers if I must start the sequence with a non-prime?
Question 7: (1 point)
Suppose you use 1,2,..., 9 to create a 2-digit password,
How many possible combination of passwords are you able to create?
(Repetitions are allowed.)
(a) 72
(b) 137
(c) 81
(d) 18
(e) 2
Question 8: (1 point)
At a wedding reception, the bride and groom and 8 attendants will form a receiving line.
How many ways can they be arranged in each of the following cases?
a) Any order will do.
The number of ways is: ____________
b) The bride and groom must be the last two in line.
The number of ways is: ____________
c) The groom must be last in line with the bride next to him.
The number of ways is: ____________
Question 9: (1 point)
Subject identification numbers in a certain scientific research project consist of three digits followed by three letters and then three more digits. Assume repetitions are not allowed within any of the three groups, but digits in the first group of three may occur also in the last group of three. Determine the number of distinct identification numbers.
The number of distinct identification numbers is: ____________
Question 10: (1 point)
Determine the number of distinguishable arrangements of the letters of the word:
AGGRESSIVENESS
There are ____________ distinguishable arrangements.
(Provide your answer as an integer)
Question 11: (1 point)
How many different pairs of people can you select from a group of 7 persons, if the order of selection does not matter?
(That is selecting A then B is considered the same as selecting B then A.)
Question 12: (1 point)
How many ways can a male and a female be selected to decorate for a party from a club consisting of ten members where 3 are men and 7 are women?
The total number of ways a male and a female can be selected is ____________
(Provide your answer as an integer)
Question 13: (1 point)
An electronics store receives a shipment of 21 graphing calculators, including 8 that are defective.
Five of the calculators are selected to be sent to a local high school.
How many of these selections will contain no defective calculators?
The number of ways to choose all slections that contain no defective calculators is: ____________
Question 14: (1 point)
How many possible 5-card hands from a standard 52-card deck would consist of the following cards?
(In a standard deck, there are 4 suits- Spades, Diamonds, Clubs and Hearts (13 cards of each suit).
Spades and Clubs are black and Hearts and Diamonds are red;
Each suit also contains 3 face cards each, for a total of 12 face cards in a deck.)
a) two diamonds and three non-diamonds
The number of 5-card hands is: ____________
b) two face cards and three non-face cards
The number of 5-card hands is: ____________
c) Three red cards, one spade, and one club
The number of 5-card hands is: ____________
Question 15: (1 point)
An urn contains 25 white balls and 20 red balls. Three balls are selected.
In how many ways can the 3 balls be drawn from the total of 45 balls:
a) If 1 is white and 2 are red?
The number of ways is: ____________
b) If all 3 balls are white?
The number of ways is: ____________
c) If all 3 balls are red?
The number of ways is: ____________

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.

Question 1: (1 point)

When two fair dice are rolled, there are 36 possible outcomes. How many possible outcomes would there be if six fair dice were rolled?

There would be ______6^6______ possible outcomes.

Question 2: (1 point)

Evaluate the following expressions:

a) 10P6

The answer is ______151200______

(Type an integer or a simplified fraction)...