Question 1
How many distinct arrangements can be made using all the letters in the word LEVEL?
- A10
- B20
- C30
- D120
Show answer
Answer: C — 30
LEVEL has 5 letters with repeated twice and repeated twice. The number of distinct arrangements is .
Study on the fly›ACT›Mathematics › Counting, combinations, and permutations
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Counting, combinations, and permutations — ACT practice questions
Counting, combinations, and permutations on the ACT Mathematics test covers how many ways objects can be selected or arranged, including overlapping sets, unordered groups, and sequences that may contain repeated items. A student must find how many people belong to at least one category after adjusting for those in both, distinguish choosing a pair from listing ordered lineups, and count distinct rearrangements of letters when some letters repeat. Questions typically appear as short word problems with a single numeric result among five answer choices. Common traps include double-counting the overlap, using permutations when order does not matter, and treating identical letters as if they were all different.
- Section: Mathematics 45 questions on the paper
- 43 practice questions in the app
Sample questions
Question 2
Naomi will attend 2 of 9 workshops. How many different pairs of workshops can she choose?
- A18
- B36
- C72
- D81
Show answer
Answer: B — 36
The order of the 2 selected workshops does not matter, so use a combination. There are selections.
Question 3
Of 50 students, 26 joined robotics, 18 joined drama, and 7 joined both groups. How many students joined at least one of the groups?
- A30
- B33
- C37
- D44
Show answer
Answer: C — 37
Adding the two group counts includes the 7 students in both groups twice. Inclusion-exclusion gives .
Practice 43 Counting, combinations, and permutations questions in the app
More ACT topics
Mathematics
- Real number system and number properties
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Polynomial expressions and factoring
- Quadratic equations
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
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