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FRM Part I Probability & Combinatorics Questions
Practise probability & combinatorics (mathematics) for the Financial Risk Manager Part I: 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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Q1.4 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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Q2.In how many ways can the letters of the word PENCIL be arranged?
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Answer: A — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q3.In how many ways can the letters of the word SQUARE be arranged?
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Answer: A — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q4.In how many ways can the letters of the word MOTHER be arranged?
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Answer: C — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q5.In how many ways can the letters of the word TABLE be arranged?
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Answer: C — 120
All 5 letters are different, so arrangements = 5! = 120.
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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 7 people?
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Answer: A — 35
Order does not matter → combinations: 7C4 = 7! / (4!·3!) = 35.
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Q8.A card is drawn from a well-shuffled deck of 52. What is the probability that it is an ace or a king?
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Answer: A — 2/13
There are 8 such cards in 52, so P = 8/52 = 2/13.
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Q9.Two fair dice are thrown. What is the probability that the sum is 4?
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Answer: D — 1/12
3 of the 36 equally likely outcomes give a sum of 4, so P = 3/36 = 1/12.
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Q10.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.
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 FRM Part I
Financial Risk Manager Part I — conducted by Global Association of Risk Professionals (GARP). Foundations of risk management, quantitative analysis, markets and valuation.
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.
FRM Part I practice topics
| Topic | Section | Question source |
|---|---|---|
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Accounting & Finance | Finance | Calculated + question bank |
| Simple & Compound Interest | Quantitative aptitude | Calculated (new numbers every set) |
| Averages & Statistics | Quantitative aptitude | Calculated (new numbers every set) |