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EJU Mathematics Probability & Combinatorics Questions
Practise probability & combinatorics (mathematics) for the Examination for Japanese University Admission — Mathematics: 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 a committee of 2 be chosen from 7 people?
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Answer: C — 21
Order does not matter → combinations: 7C2 = 7! / (2!·5!) = 21.
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Q2.2 fair coins are tossed. What is the probability of at least one head?
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Answer: D — 3/4
P(no head) = (1/2)^2 = 1/4; P(at least one head) = 1 − 1/4 = 3/4.
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Q3.In how many ways can the letters of the word PLANET be arranged?
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Answer: C — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q4.3 fair coins are tossed. What is the probability of at least one head?
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Answer: C — 7/8
P(no head) = (1/2)^3 = 1/8; P(at least one head) = 1 − 1/8 = 7/8.
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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.In how many ways can a committee of 2 be chosen from 10 people?
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Answer: D — 45
Order does not matter → combinations: 10C2 = 10! / (2!·8!) = 45.
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Q7.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: B — 2/13
There are 8 such cards in 52, so P = 8/52 = 2/13.
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Q8.In how many ways can a committee of 3 be chosen from 11 people?
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Answer: A — 165
Order does not matter → combinations: 11C3 = 11! / (3!·8!) = 165.
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Q9.In how many ways can the letters of the word SQUARE 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 a committee of 2 be chosen from 11 people?
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Answer: A — 55
Order does not matter → combinations: 11C2 = 11! / (2!·9!) = 55.
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 EJU Mathematics
Examination for Japanese University Admission — Mathematics — conducted by Japan Student Services Organization (JASSO). Taken by international students applying to Japanese universities.
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.
EJU Mathematics practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |