UPSC Prelims 2007 · General Studies
Question 137: Basic Numeracy
Five balls of different colours are to be placed in three different boxes such that any box contains at least one ball. What is the maximum number of different ways in which this can be done?
AnswerThe answer is (c).
Count the ways to send 5 distinct balls into 3 distinct boxes with no box empty. All placements give 3^5 = 243. Subtract those leaving a box empty: 3 x 2^5 = 96, then add back the cases with two boxes empty, counted twice: 3. So 243 - 96 + 3 = 150. Check by splitting: 3-1-1 gives 3 x 10 x 2 = 60 and 2-2-1 gives 3 x 5 x 6 = 90, total 150.
Why each option is right or wrong
- (a) 90 is too small; the count is 150.
- (b) 120 is too small; the count is 150.
- (c) Correct: 243 - 96 + 3 = 150.
- (d) 180 is too large; the count is 150.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2007, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.