UPSC Prelims 2015·CSAT·Quantitative Aptitude·Combinatorics and Probability

A student has to opt for 2 subjects out of 5 subjects for a course, namely, Commerce, Economics, Statistics, Mathematics I and Mathematics II. Mathematics II can be offered only if Mathematics I is also opted. The number of different combinations of two subjects which can be opted is

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Last updated 8 Jul 2026, 4:39 pm IST
  1. A5
  2. B6
  3. C7Correct
  4. D8

Explanation

To find the total number of combinations, we evaluate all possible pairs of the five subjects: Commerce (C), Economics (E), Statistics (S), Mathematics I (M1), and Mathematics II (M2).

First, let us list the combinations that do not involve Mathematics II. Since there are 4 subjects (C, E, S, M1), the number of ways to choose 2 is 6. These pairs are:

  1. Commerce and Economics
  2. Commerce and Statistics
  3. Commerce and Mathematics I
  4. Economics and Statistics
  5. Economics and Mathematics I
  6. Statistics and Mathematics I

Next, we consider combinations involving Mathematics II. The rule states that Mathematics II can only be opted if Mathematics I is also opted. This means there is only 1 possible pair involving Mathematics II: 7. Mathematics I and Mathematics II

Any other combination with Mathematics II (such as Mathematics II and Commerce) is invalid because Mathematics I is missing.

Adding these together, we get 6 plus 1, which equals 7 total combinations. Therefore, option C is correct.

Quantitative Aptitude: A student has to opt for 2 subjects out of 5 subjects for a course, namely, Commerce, Economics, Statistics, Mathematics
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