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JEE Main Probability & Combinatorics Questions
Practise probability & combinatorics (mathematics) for the Joint Entrance Examination (Main): 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 ORANGE be arranged?
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Answer: A — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q2.Two fair dice are thrown. What is the probability that the sum is 9?
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Answer: C — 1/9
4 of the 36 equally likely outcomes give a sum of 9, so P = 4/36 = 1/9.
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Q3.A card is drawn from a well-shuffled deck of 52. What is the probability that it is a face card (J, Q, K)?
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Answer: B — 3/13
There are 12 such cards in 52, so P = 12/52 = 3/13.
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Q4.Two fair dice are thrown. What is the probability that the sum is 6?
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Answer: C — 5/36
5 of the 36 equally likely outcomes give a sum of 6, so P = 5/36 = 5/36.
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Q5.In how many ways can a committee of 2 be chosen from 7 people?
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Answer: A — 21
Order does not matter → combinations: 7C2 = 7! / (2!·5!) = 21.
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Q6.In how many ways can a committee of 4 be chosen from 7 people?
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Answer: C — 35
Order does not matter → combinations: 7C4 = 7! / (4!·3!) = 35.
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Q7.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: A — 1/13
There are 4 such cards in 52, so P = 4/52 = 1/13.
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Q8.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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Q9.In how many ways can a committee of 2 be chosen from 6 people?
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Answer: C — 15
Order does not matter → combinations: 6C2 = 6! / (2!·4!) = 15.
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Q10.In how many ways can a committee of 2 be chosen from 10 people?
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Answer: B — 45
Order does not matter → combinations: 10C2 = 10! / (2!·8!) = 45.
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 JEE Main
Joint Entrance Examination (Main) — conducted by National Testing Agency (NTA). India’s national engineering entrance for NITs, IIITs and other institutes, and the qualifier for JEE Advanced.
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.
JEE Main practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Physics | Science | Calculated + question bank |
| Chemistry | Science | Calculated + question bank |