UPSC Prelims 2015 · CSAT
Question 49: Basic Numeracy
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
AnswerUPSC’s answer is (c).
Without any restriction, 2 subjects out of 5 give 5C2 = 10 combinations. The restriction removes pairs that include Mathematics II without Mathematics I. Those are Mathematics II with Commerce, with Economics, or with Statistics: 3 pairs. So 10 − 3 = 7. Check by listing: pairs among the four subjects other than Mathematics II give 6, plus Mathematics I with Mathematics II gives 1, total 7.
Why each option is right or wrong
- (a) Wrong: 5 is below the 7 valid pairs.
- (b) Wrong: 6 counts only the pairs without Mathematics II and misses the Mathematics I plus II pair.
- (c) Right: 10 − 3 = 7.
- (d) Wrong: 8 would wrongly allow one of the three barred pairs with Mathematics II alone.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2015, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.