UPSC Prelims 2021 · CSAT
Question 69: Basic Numeracy
There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place ?
AnswerUPSC’s answer is (b).
Number the persons 1 to 6 and choose 3 positions with no two adjacent. List by smallest position: 1, 3, 5; 1, 3, 6; 1, 4, 6; and 2, 4, 6. Starting at 3 or later leaves too few non-adjacent positions. That is 4 ways. A formula agrees: choosing k = 3 non-adjacent items from n = 6 gives C(n − k + 1, k) = C(4, 3) = 4. Remember: for non-adjacent choices, list systematically or use C(n − k + 1, k).
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.
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) 3 misses one of the four sets (1, 3, 5), (1, 3, 6), (1, 4, 6), (2, 4, 6).
- (b) Right: the four sets are 1-3-5, 1-3-6, 1-4-6 and 2-4-6.
- (c) 5 would need a fifth non-adjacent set, and none exists.
- (d) 6 would need two more sets, and none exists.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.