Basic Counting
Permutations/Combinations
Complementary Counting
Counting Shapes and Paths
100
The number of ways that a number can be chosen from 1 to 22 such that it is a multiple of 3 or 8 |
What is 9?
100
The number of ways that the letters in the word "WORD" can be arranged.
What is 24?
100
The Dr. Seuss story The Cat in the Hat contains 236 distinct words, 1 of which has three syllables and 14 of which have two syllables. The rest of the words have only one syllable.
The number of words that have only one syllable.
What is 221?
100
The maximum number of intersection points between three circles.
What is 6?
200
A student has to take one course of physics, one of science and one of mathematics. He may choose one of 3 physics courses, one of 2 science courses and one of 2 mathematics courses.
The number of ways this student can select the 3 courses he has to take.
What is 12?
200
The number of ways you can choose 3 numbers from a group of 9 numbers.
What is 84?
200
The number of ways a number can be chosen from 1 to 22 such that it is a multiple of 2 or 3
What is 15?
200
Eric starts at (0,0) on the coordinate plane and wishes to move to the point (4,3). He must stay on the grid lines and move either one unit up or one unit right.
The number of ways that he can move to the point (4,3).
What is 35?
300
Danny flips a fair coin 6 times.
The total number of possible outcomes. (For example, one outcome is HHTHTT)
What is 64?
300
The number of ways that the letters in the word "HAPPY" can be arranged.
What is 60?
300
How many three digit numbers have at least two digits that are the same?
What is 252?
300
The number of squares in this image: 
What is 30?
400
Roslyn has ten boxes. Six of the boxes contain pencils, three of the boxes contain pens, and two of the boxes contain both pens and pencils.
The number of boxes that contain neither pens nor pencils.
What is 3?
400
Elise has one book each for algebra, geometry, history, psychology, Spanish, English, and physics in her locker.
The number of different sets of three books she could choose.
What is 35?
400
The number of integers in the first 100 positive integers that are not perfect squares or cubes.
What is 88?
400
The number of triangles you can draw whose vertices are on a 3x2 grid of dots.
What is 18?
500
The number of outcomes of a roll of two dice that results in a sum that is a prime number. (Rolling a 3 and a 4 is the same as rolling a 4 and a 3)
What is 8?
500
My school's math club has 6 boys and 8 girls. I need to select a team to send to the state math competition. We want 6 people on the team.
The number of ways the team can be selected so that it has more girls than boys.
What is 1414?
500
Four pairs of twins and 12 non-twins attend a birthday party. Each kid high-fives everyone else except their twin, if they have one.
The number of high-fives there are.
What is 186?
500
John walks six blocks on a city grid of sidewalks to his favorite deli for lunch: three blocks north and three blocks west. He never uses the same exact path on his return to work. He always stays on the city sidewalks and goes six blocks each way.
The number of different ways John can walk to the deli and back.
What is 380?