UPSC Prelims 2008 · General Studies
Question 6: Basic Numeracy
A schoolteacher has to select the maximum possible number of different groups of 3 students out of a total of 6 students. In how many groups any particular student will be included?
AnswerThe answer is (c).
The number of different groups of 3 from 6 students is 6C3 = 20. A particular student is in a group when the other two members are chosen from the remaining 5 students, which can be done in 5C2 = 10 ways. As a check, 20 groups of 3 give 60 places shared among 6 students, which is 10 per student.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) 6 is just the number of students, not the number of groups containing one of them.
- (b) 8 does not match 5C2 = 10 groups containing a given student.
- (c) Choosing the other 2 members from 5 students gives 5C2 = 10 groups.
- (d) 12 is more than 5C2 = 10; the check 20 x 3 / 6 also gives 10.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2008, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.