Basic Combinatorics
Imani has homework assignments in five subjects. She only has time to do three of them. How many possibilities are there for which assignments she completes?
Combination: 10
(x+y)4
x4+4x3y+6x2y2+4xy3+y4
You roll a fair six-sided die. What is the probability that the die shows a one or a four?
1/3=0.333
A spinner has an equal chance of landing on each of its four numbered regions. You spin twice. What is the probability of the first spin landing in region three and the second spin landing in region three?
1/16 = 0.063
A gambler places a bet on a horse race. To win, she must pick the top three finishers in any order. Thirteen horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win her bet?
0.35%
(2x+y)5
32x5+80x4y+80x3y2+40x2y3+10xy4+y5
A small pond contains six catfish and two bluegill. If six fish are caught at random, what is the probability that all of them are catfish?
3.571%
A cooler contains twelve bottles of sports drink: four lemon-lime flavored and eight orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. What is the probability that your friend gets a lemon-lime and you get an orange?
8/33 = 0.242
When a button is pressed, a computer program outputs a random even number greater than 0 and less than 8. You press the button six times. Find the number of possible outcomes in the sample space.
729 (3^6)
(x-3y)4
x4-12x3y+54x2y2-108xy3+81y4
A test consists of six true/false questions. A student who forgot to study guesses randomly on every question. What is the probability that the student answers exactly three questions correctly?
31.25%
There are four nickels and five dimes in your pocket. Two of the nickels and four of the dimes are Canadian. The others are US currency. You randomly select a coin from your pocket. What is the probability that it is a dime or is US currency?
7/9=0.778
Beth and Ashley are planning trips to three countries this year. There are 13 countries they would like to visit. One trip will be one week long, another two days, and the other two weeks. How many possible itineraries are there?
Permutations: 1,716
(2x-3y)5
32x5-240x4y+720x3y2-1080x2y3+810xy4-243y5
A six-sided die is rolled seven times. What is the probability that the die will show an even number at most five times?
93.75%
Your sock drawer has four white socks, four brown socks, and six black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot.
8/91 = 0.0888
A group of 21 people need to take an elevator to the top floor. They will go in groups of seven. They are deciding who will take the elevator on its second trip. How many possibilities are there?
Combination: 116,280
(a2-2b)6
An archer has a 30% chance of hitting the bullseye on a target. What is the probability that the archer will hit the bullseye exactly two out of six times?
32.414%
A basket contains four apples, five peaches, and five pears. You randomly select and eat three pieces of fruit. The first piece of fruit is an apple and the next two pieces are peaches.
10/273 = 0.037