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NDA Probability & Combinatorics Questions
Practise probability & combinatorics (mathematics) for the National Defence Academy & Naval Academy Examination: 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: A — 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 SQUARE be arranged?
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Answer: B — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q3.2 fair coins are tossed. What is the probability of at least one head?
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Answer: C — 3/4
P(no head) = (1/2)^2 = 1/4; P(at least one head) = 1 − 1/4 = 3/4.
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Q4.In how many ways can the letters of the word TABLE be arranged?
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Answer: A — 120
All 5 letters are different, so arrangements = 5! = 120.
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Q5.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: C — 2/13
There are 8 such cards in 52, so P = 8/52 = 2/13.
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Q6.In how many ways can a committee of 2 be chosen from 9 people?
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Answer: D — 36
Order does not matter → combinations: 9C2 = 9! / (2!·7!) = 36.
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Q7.A card is drawn from a well-shuffled deck of 52. What is the probability that it is a heart?
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Answer: C — 1/4
There are 13 such cards in 52, so P = 13/52 = 1/4.
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Q8.Two fair dice are thrown. What is the probability that the sum is 8?
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Answer: A — 5/36
5 of the 36 equally likely outcomes give a sum of 8, so P = 5/36 = 5/36.
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Q9.In how many ways can the letters of the word GARDEN 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 4 be chosen from 9 people?
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Answer: C — 126
Order does not matter → combinations: 9C4 = 9! / (4!·5!) = 126.
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 NDA
National Defence Academy & Naval Academy Examination — conducted by Union Public Service Commission (UPSC). Entry to the tri-service National Defence Academy after Class 12, with Mathematics and General Ability papers.
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.
NDA 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 |
| English Grammar | English | Question bank |