UPSC Prelims 2006 · General Studies
Question 137: Basic Numeracy
Each of 2 women and 3 men is to occupy one chair out of 8 chairs, each of which is numbered from 1 to 8. First, women are to occupy any two chairs from those numbered 1 to 4; and then 3 men would occupy any three chairs out of the remaining 6 chairs. What is the maximum number of different ways in which this can be done?
AnswerThe answer is (c).
Treat the two women as distinct. They can take chairs from 1-4 in 4 x 3 = 12 ways. The three men then take 3 of the 6 remaining chairs in 6 x 5 x 4 = 120 ways (each man being distinct). So the total is 12 x 120 = 1,440.
Why each option is right or wrong
- (a) 40 does not match the count.
- (b) 132 does not match the count.
- (c) Correct: 12 x 120 = 1,440.
- (d) 3660 does not match the count.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.