UPSC Prelims 2015 · CSAT
Question 69: Basic Numeracy
There are 5 tasks and 5 persons. Task-1 cannot be assigned to either person-1. or person-2. Task-2 must be assigned to either person-3 or person-4. Every person is to be assigned one task. In how many ways can the assignment be done ?
AnswerUPSC’s answer is (c).
Task 2 must go to person 3 or 4: 2 ways. Task 1 cannot go to person 1 or 2, and cannot go to the person already given task 2, so it can go to one of the other two among persons 3, 4 and 5: 2 ways. The remaining 3 tasks go to the 3 remaining persons freely: 3! = 6 ways. Total = 2 × 2 × 6 = 24.
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) Wrong: 6 counts only the free assignments of the last three tasks.
- (b) Wrong: 12 undercounts the arrangements of the last three tasks.
- (c) Right: 2 × 2 × 6 = 24.
- (d) Wrong: 144 is more than the 120 assignments possible even without restrictions.
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.