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GRE Probability & Combinatorics Questions
Practise probability & combinatorics (mathematics) for the GRE General Test: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Probability & Combinatorics practice
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Q1.In how many ways can the letters of the word SQUARE be arranged?
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Answer: C — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q2.3 fair coins are tossed. What is the probability of at least one head?
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Answer: B — 7/8
P(no head) = (1/2)^3 = 1/8; P(at least one head) = 1 − 1/8 = 7/8.
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Q3.In how many ways can the letters of the word PENCIL be arranged?
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Answer: B — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q4.In how many ways can a committee of 4 be chosen from 10 people?
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Answer: C — 210
Order does not matter → combinations: 10C4 = 10! / (4!·6!) = 210.
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Q5.4 fair coins are tossed. What is the probability of at least one head?
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Answer: D — 15/16
P(no head) = (1/2)^4 = 1/16; P(at least one head) = 1 − 1/16 = 15/16.
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Q6.A card is drawn from a well-shuffled deck of 52. What is the probability that it is a king?
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Answer: B — 1/13
There are 4 such cards in 52, so P = 4/52 = 1/13.
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Q7.In how many ways can a committee of 4 be chosen from 6 people?
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Answer: A — 15
Order does not matter → combinations: 6C4 = 6! / (4!·2!) = 15.
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Q8.In how many ways can a committee of 2 be chosen from 7 people?
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Answer: D — 21
Order does not matter → combinations: 7C2 = 7! / (2!·5!) = 21.
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Q9.In how many ways can the letters of the word PLANET be arranged?
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Answer: D — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q10.In how many ways can the letters of the word MOTHER be arranged?
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Answer: A — 720
All 6 letters are different, so arrangements = 6! = 720.
How to approach probability & combinatorics questions
Probability = favourable ÷ total outcomes. List small sample spaces (two dice = 36 outcomes). Use nPr when order matters and nCr when it does not; divide by repeats for repeated letters.
About GRE
GRE General Test — conducted by Educational Testing Service (ETS). Graduate admission test with Verbal Reasoning, Quantitative Reasoning and Analytical Writing.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
GRE practice topics
| Topic | Section | Question source |
|---|---|---|
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Data Interpretation | Data interpretation | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Vocabulary & Idioms | English | Question bank |