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
- (a) 5
- (b) 6
- (c) 7 ✓ UPSC's answer
- (d) 8
Why the answer is (c)
• Without any restriction, 2 subjects can be picked from 5 in 5C2 = 10 ways.
• Mathematics II is allowed only with Mathematics I, so the pairs Commerce–Maths II, Economics–Maths II and Statistics–Maths II are ruled out.
• Valid pairs = 10 − 3 = 7 (the six pairs from Commerce, Economics, Statistics and Maths I, plus Maths I–Maths II).
• Hence option (c).
Why the other options are wrong
- (a) 5
- 5 misses two valid pairs.
- (b) 6
- 6 leaves out the valid pair Maths I–Maths II.
- (d) 8
- 8 wrongly admits one pair with Maths II but without Maths I.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.