Discrete
How many license plates can be made using either two uppercase English letters followed by four digits or four uppercase English letters followed by two digits?
52,457,600
On each of the 22 work days in a particular month, every employee of a start-up venture was sent a company communication. If a total of 4840 company communications were sent, how many employees does the company have, assuming that no staffing changes were made that month?
220
An office building contains 22 floors and has 37 offices on each floor. How many offices are in the building?
814
Consider people with three-letter initials. How many different three-letter initials are there with no letters repeated?
15600
How many positive integers less than 1000 are divisible by neither 7 nor 11?
779
How many strings of three decimal digits begin with an odd digit?
500
How many one-to-one functions are there from the set A to a set with 7 elements?
2520
Consider bit strings of length seven.How many bit strings of length seven either begin with two 0s or end with three 1s?
2^5 + 2^4 − 2^2
Use a tree diagram to find the number of bit strings of length four with no three consecutive 0s. How many such bit strings are there?
13
A bowl contains 10 red balls and 10 blue balls. A woman selects balls at random without looking at them. How many balls must she select to be sure of having at least three balls of the same color?
5
A bowl contains 10 red balls and 10 blue balls. A woman selects balls at random without looking at them. What is the minimum number of balls she must select to be sure of having at least three blue balls?
13
7 women and 11 men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
8106
7 women and 11 men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee?
8085
P(6, 2)
30
In how many ways can you create a two-element set where each element in the set is an positive integer less than 90?
3916
A coin is flipped where, each flip comes up as either heads or tails. How many possible outcomes contain exactly two heads if the coin is flipped 11 times?
55
Suppose that a department contains 10 men and 13 women. How many ways are there to form a committee with six members if it must have the same number of men and women?
34320
A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. How many ways are there to choose 9 croissants?
2002
A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants.How many ways are there to choose 23 croissants with no more than two broccoli croissants?
45150
How many different combinations of pennies, nickels, dimes, quarters, and half dollars can a piggy bank contain if it has 21 coins in it?
12650
How many possible outcomes contain the same number of heads and tails if the coin is flipped 10 times?
252
How many ways are there to assign three jobs to 8 employees if each employee can be given more than one job?
512
A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. How many ways are there to choose 4 dozen croissants?
2869685
A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants.How many ways are there to choose 25 croissants with at least five chocolate croissants and at least three almond croissants?
26334
How many different strings can be made from the letters in MISSISSIPPI, using all letters?
34650