WorksheetsCombinatorics (Counting Principles) Unit Review
Total questions: 50
Worksheet time: 13hrs 30mins
A box contains 10 white and 15 black marbles.
If seven marbles are picked from this box at random and without replacement, what is the probability that three are white and four are black?
0.3408
0.1988
0.0057
0.0097
How many distinguishable ways exist to arrange the letters in the word ELEMENTAL?
30,240
60,480
90,720
362,880
There are 20 randomly-selected people in a room. What is the probability at least one person in this room shares a birthday with someone else in this room? [Ignore leap years.]
41%
59%
5%
95%
There are 19 runners in a race. The top three runners will win a prize, with a different prize for 1st, 2nd and 3rd place.
How many possible outcomes exist for the awarding of these prizes? [Assume that there are no ties and that at least three runners finish the race.]
5,814
969
6,859
57
How many options does she have when making this selection?
Eight of these applicants are chosen for interviews, supposedly at random, but none of the chosen applicants were women. What is the probability that this would occur if the selection really was random?
In how many ways can this test be completed if every question must be answered?
An ATM code for a bank account consists of four digits.
Suppose that if this password is entered incorrectly more than four times in a row, the user is locked out. If a hacker tries to guess this password, what is the probability that they can successfully hack into the account?
0.0004
0.0006
0.0008
0.0013
In how many ways can the officers be chosen?
If the tiles are selected from this bag at random and placed in the order in which they were drawn, what is the probability that they spell out the word BOBBY?
A grocery store sells four types of fruit. Your mother sends you to this store and asks you to buy six pieces of fruit, but she does not say what type of fruit she wants. In how many ways can you fulfill her request?
84
210
24
4,096
If you buy 30 tickets for this lottery, each with a unique number, what is the probability that you have at least one winning ticket?
Cindy, Macy and Tracy are friends and they have all applied to go on this field trip. What is the probability that this entire group of friends gets to go on the field trip together?
In how many ways can this committee be formed?
Find P(x≤2).
How many digits are in the standard numerical system?
9
10
26
100
At summer camp, the campers pick two different activities for the first day of camp. They can choose from among hiking, canoeing, rock climbing, and bird watching.
How many different choices are there for spending the first day of camp, if the campers don't care what order they do the activities in?
6
4
16
12
How many different four-person relay teams can be chosen from eight students? Assume that each chosen person is simply "on the team," not in any special position.
24
1,680
70
40,320
Papa John's pizza offers 4 kinds of cheese, 3 types of crust, 2 types of sauce and 8 kinds of topping. How many different two-topping pizzas can be bought from Papa John's? [Assume that choices such as "double pepperoni" count as two-topping pizzas.]
384
864
1,536
1,344
How many 5-digit (numerical) passwords are possible for the school email system if the first digit cannot be 0?
11,424,400
10,967,424
9,000
90,000
This symbol means "the product of"
Σ
Π
!
Λ
Multiplying together all of the natural numbers between 1 and "n" results in a product called a/an...
factorial
distinguishable
stars and bars
subset
This symbol means "the factorial of"
Σ
Π
!
Λ
This is the symbol for the size of the selection set.
n
r
!
Π
This is the symbol for the number of selections that are made.
n
r
!
Π
Review: About what percent of heights in this data set are between 60 inches and 66 inches?
75%
50%
100%
25%
Review: 479 freshman took an Algebra test. The scores had a mean of 68 and a standard deviation of 6. At least how many students scored between 56 and 80?
403
360
440
240
Review: You are taking a class in which your grade is determined from five sources: 50% from your test mean, 15% from your midterm, 20% from your final exam, 10% from computer lab work, and 5% from your homework. Your scores are 86 (test mean), 96 (midterm), 82 (final exam), 98 (computer lab), and 100 (homework). What is the weighted mean?
90.2
89.7
88.6
87.87
Review: The school district is interested in finding out student and parent opinions about the dress code. They obtain a list of students from each school in the district and put them in alphabetical order. They then send a survey to every 25th student and their parents on the list.
What sampling method did the district use?
Simple Random
Stratified
Systematic
Convenience
Review: A doctor is conducting a study on a new drug in which some patients receive the experimental drug and others receive a sugar pill. None of the patients know which pill they received. Some of the patients who received the sugar pill reported that the drug was working. This is an example of what phenomenon?
Placebo Effect
Margin of Error
Outlier
Randomization
Review: The following question was included in a survey.
"Most Americans prefer to purchase products manufactured in the United States. Do you prefer to purchase products manufactured in the United States?"
Which of the following would be the best way to reword this leading question to make it unbiased?
Products made in the USA are better.
Agree or Disagree?
Production in many other nations has been known exploit workers. Do you prefer to buy products made in other countries or in the US?
Products made in the US have been proven to last longer than imported products. Do you prefer to buy US made products or imported products?
Where do you prefer products you purchase to be manufactured?
Review: The mean lifespan of a tire in the UK is 30,000 km. with a standard deviation of 2,000 km.
Therefore, at least 68% of all tires in the UK will have a lifespan between ___________ km and __________ km.
26,464 km and 33,536 km.
23,750 km and 36,250 km.
26,000 km and 34,000 km.
27,251 km and 30,749 km.
Order matters for which of the following types of sample space? [Check all that apply.]
Power
Permutation
Multiset
Combination
Distinguishable Permutation
Order doesn't matter for which of the following types of sample space? [Check all that apply.]
Power
Permutation
Multiset
Combination
Distinguishable Permutation
Selections are made with replacement for which of the following types of sample space? [Check all that apply.]
Power
Permutation
Multiset
Combination
Distinguishable Permutation
Selections are made without replacement for which of the following types of sample space? [Check all that apply.]
Power
Permutation
Multiset
Combination
Distinguishable Permutation
Which of the following are characteristics of a distinguishable permutation? [check all that apply.]
n=r
some items in the selection set are identical
selections are made with replacement
order matters
Review: A shareholder argues that a company's CEO is overpaid. The mean salary for CEOs in this industry is $4.6 million per year with a standard deviation of $1.2 million.
If this CEO has a salary of $8.2 million per year, what is the z-score of this salary? Is this salary unusual?
z=3.00; Yes, unusual
z=1.78; No, not unusual
z=3.00; No, not unusual
z=1.78; Yes, unusual
Review: A bag of marbles has four different colors of marble inside.
Suppose a trial consists of picking a single marble at random from this bag. What is the missing probability if given this list?
Green: 20%
Red: 30%
Blue: 10%
Yellow: _____
5%
20%
30%
40%
A scrabble bag contains two "E" tiles, two "L" tiles, one "R" tile, one "S" tile, and one "Y" tile.
If these tiles are drawn randomly from the bag and placed in the order in which they were drawn, what is the probability that they spell the word YELLERS?
0.0008
0.0002
0.1429
0.0204
