Counting
Venn Diagrams
Combinations
Permutations
Probability
100
You own 4 shirts and 5 pairs of pants. How many different outfits can you make?
4*5 =20
100
In the Venn Diagram above, how many are in set A?
25
100
Find the value of: 5C2
(5!)/(2!3!) =10
100
Find the value of: 5P2
20
100
Construct a probability model for the experiment: tossing a fair coin, then a fair die.
{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}; each probability = 1/12
200
An ice cream shop sells customizable sundaes. They offer 8 types of ice cream flavors, 6 types of toppings, and 4 types of syrups. How many different sundaes can the shop make assuming each sundae has one type of ice cream, one type of topping, and one type of syrup?
8*6*4=192
200
In the Venn Diagram above, how many are in set A or B?
37
200
How many different ways can 3 items be chosen from a group of 6 items?
6C3 = 20
200
In how many ways can a squad of 4 relay runners be chosen from a track team of 8 runners?
1,680
200
Two fair 6-sided dice are rolled. What is the probability of rolling a sum of 6 or a sum of 8?
10/36 = 5/18
300
A government issues license plates with 3 letters (A-Z) followed by 3 digits (0-9). How many different combinations are possible if letters can be repeated but digits cannot?
26*26*26*10*9*8=12,654,720
300
In the Venn Diagram above, how many are in set A or B but not C?
28
300
How many ways can a committee of 5 professors be chosen from a department having 12 professors?
12C5 = 792
300
A 10k road race has 12 runners. How many different ways can 1st, 2nd, and 3rd places be awarded?
12P3 = 1,320
300
Using the spinners shown above, spin Spinner I, then Spinner II, then Spinner III. What is the probability of getting a 3, followed by a Yellow or Red, followed by a Backward? Leave your answer as a simplified fraction
1/4*2/3*1/2 = 2/24 = 1/12
400
How many different 10-letter words (real and imaginary) can be formed by the letters in the word STRESSLESS ?
(10!)/(2!5!) = 15,120
400
In a survey of 100 people, 40 owned a cat, 50 owned a dog, 25 owned another kind of pet ("other"), 25 owned a cat and a dog, 10 owned a cat and another kind of pet, 15 owned a dog and another kind of pet, and 5 owned all three. How many people in the survey did not own a dog, cat, or another kind of pet?
30
400
A group consists of 7 men and 9 women. A committee of 4 is to be formed from this group. How many committees can be formed that contain no more than 1 man?
(7C0 * 9C4) + (7C1 * 9C3) = 126 + 588 = 714
400
If 4 people enter a bus having 9 vacant seats, in how many ways can they be seated?
3,024
400
In a certain lottery, there are 6 balls, numbered 1, 2, 3, 4, 5, 6. Of these, 4 are drawn in order. If you pick 4 numbers that match those drawn in the correct order, you win $10,000. What is the probability of winning such a lottery? Leave your answer as a simplified fraction.
1/6*1/5*1/4*1/3 = 1/360
500
The chart below represents the marital status of females 18 years old and older in 2007.
Determine the number of females 18 years old or older who are married, widowed, or divorced.
88,008 (in thousands)
500
In a survey of 100 people, 40 owned a cat, 50 owned a dog, 25 owned another kind of pet ("other"), 25 owned a cat and a dog, 10 owned a cat and another kind of pet, 15 owned a dog and another kind of pet, and 5 owned all three. How many people in the survey owned a dog or a cat, but not another kind of pet?
45
500
A combination lock displays 50 numbers. To open it, you turn to a number, then rotate clockwise to a second number, and then counterclockwise to a third number. How many different lock combinations are there?
125,000 if you can turn back to the same number; 117,600 if you cannot turn back to the same number
500
How many ways can 12 people have the same birthday? Assume that a year has 365 days.
4.65743... x 1030
500
What is the probability that at least 2 people have the same birthday in a group of 12 people? Assume that there are 365 days in a year.
0.167