Counting Principles
A club has 10 members. How many different ways can they elect a President, Vice President, and Secretary?
720
A bag contains 5 red marbles and 7 blue marbles. If one marble is drawn, what is the probability that it is red OR blue?
1
A committee of 3 people is to be formed from a group of 5 men and 4 women. What is the probability that the committee consists of 3 women?
1/21
A gardener has 8 different types of flower seeds. If they want to plant exactly 3 types in a row along a fence, how many different arrangements are possible?
336
Also known as Leonardo of Pisa, this famous Italian mathematician is best known for discovering a sequence where each number is the sum of the two previous numbers.
Fibonacci
In how many ways can the letters in the word 'MATH' be rearranged?
24
You roll a fair six-sided die twice. What is the probability of rolling a 4 on the first roll AND an even number on the second roll?
1/12
A basketball player has a $70\%$ free-throw success rate. If she shoots 5 free throws, what is the probability she makes exactly 4 of them? (Round to the nearest percent)
36%
If P(A) = 0.5 and P(B) = 0.2, and events A and B are independent, what is P(A and B)?
0.1
This value represents the sum of the first five prime numbers.
28
Find the number of distinguishable permutations of the letters in BASKETBALL.
453,600
If P(A) = 0.3, P(B) = 0.4, and events A and B are mutually exclusive, what is P(A or B)?
0.7
A class has eight boys and four girls. If the teacher randomly picks eight students, what is the probability that she will pick all boys? (express a fraction)
1/495
A box contains 6 green pens and 4 black pens. If you pick 3 pens at random, what is the probability that all 3 are green? (express as a fraction in simplest form)
1/6
In this 1997 film, Matt Damon’s character plays a Harvard janitor who is also a natural genius in mathematics.
Good Will Hunting
Suppose you seat 6 people at a circular table. How many different arrangements are possible?
120
A card is drawn from a standard deck of 52 cards. What is the probability that it is a King OR a Heart? (Round to the nearest percent)
31%
Which of the following is a requirement for a binomial distribution?
A. The number of trials is infinite.
B. The trials must be independent.
C. There must be at least 3 possible outcomes.
D. The probability of success must change each trial.
B
A box contains 10 functional widgets and 4 defective widgets. If 2 widgets are randomly selected without replacement, what is the setup for the probability that both are defective? (Express a percent rounded to nearest tenth)
6.6%
In this 2001 film, Russell Crowe plays real-life mathematician, John Nash, who is best known for his contributions in the field of game theory.
A Beautiful Mind
A student has 7 books but only has room for 3 on a small shelf. If the order of the books on the shelf matters, how many ways can the shelf be arranged?
210
A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a heart or a jack? (express as a fraction)
4/13
A jar contains 4 white chips and 6 black chips. Two chips are drawn without replacement. What is the probability that both are black? (express as a fraction in lowest terms)
1/3
A bag has 5 red, 5 blue, and 5 yellow balls. If you grab 3 balls, what is the probability you get exactly one of each color? (express as a percent rounded to nearest tenth)
27.5%
During the math competition scene in the movie “Mean Girls,” the answer to the calculus problem “what is the limit as x approaches zero of [ln(1-x)-sinx]/(1-cos²x)” is this.
"The Limit Does Not Exist!"