UPSC Prelims 2010 · General Studies
Question 115: Basic Numeracy
When ten persons shake hands with one another, in how many ways is it possible ?
AnswerThe answer is (d).
A handshake is between two persons and each pair shakes hands once. The number of handshakes among 10 persons is the number of ways to choose 2 from 10: 10 x 9 / 2 = 45. Remember: pairs from n = n(n - 1) / 2; computing 10 x 9 = 90 counts each handshake twice.
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) 20 has no basis in the count.
- (b) 25 has no basis in the count.
- (c) 40 has no basis in the count.
- (d) Right: 10C2 = 45.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2010, General Studies, Series A. The paper on upsc.gov.in.