Basic Counting
Permutations/Combinations
Complementary Counting
Probability
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

What is the probability of rolling an odd number on a standard 6-sided dice?

1/2

200

A student has to take one course of science, one of history, and one of mathematics. He may choose one of 3 science courses, one of 2 history 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

What is the chance of pulling out a black marble from a bag that has 3 black marbles, 5 red marbles, and 2 green marbles?

3/10

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

What is the chance of drawing a jack from a standard deck of cards (52 cards)?  There are 4 jacks in a standard deck of cards.

1/13

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

What is the probability of getting a sum of 10 using 2 standard 6-sided dice?

1/12

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

What is the probability of flipping heads on a coin 3 times in a row?

1/8

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