IPMAT · Quantitative Ability

Permutations, combinations, probability and sets

Counting, probability, sets and Venn counting.

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About this topic in IPMAT

  • In the exam pattern: IIM Rohtak IPM Aptitude Test (2026), Quantitative Ability: 40 questions, 160 marks (IIM Rohtak notice, read 26 Oct 2026).
  • Next exam day: IPMAT Indore 2027 exam (expected): 8 May 2027 (Expected — an estimate, not announced).

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  • Q1 · Permutations, combinations, probability and sets · MEDIUM

    A committee of 4 members is to be formed from a group of 4 men and 5 women. The committee must include at least 2 women. How many different committees can be formed?

  • Q2 · Permutations, combinations, probability and sets · MEDIUM

    In a group of 50 students, 20 play Cricket, 15 play Football, and 10 play Basketball. It is known that 5 students play both Cricket and Football, 4 play both Football and Basketball, and 3 play both Cricket and Basketball. If 2 students play all three games, how many students do not play any of these three games?

  • Q3 · Permutations, combinations, probability and sets · EASY

    A fair die is rolled twice. What is the probability that the sum of the numbers obtained is a prime number?

  • Q4 · Permutations, combinations, probability and sets · EASY

    How many distinct 4-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if no digit is repeated?

  • Q5 · Permutations, combinations, probability and sets · MEDIUM

    A bag contains 3 red balls and 4 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are of the same color?

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