UPSC Civil Services 2022 Prelims General Studies Paper II

Case 1: When we have 3 coffee cups in one row, 2 coffee cups in another row, and 1 coffee cup in the remaining row (3!).
For row having 3 coffee cups arrangement can be done in only one way.
For row having 2 coffee cups arrangement can be done in three ways.
For row having 1 coffee cup arrangement can be done in three ways.
Total arrangements for case 1=3!×1×3×3=54.
Case 2: When we have 2 coffee cups in each row (1).
Each row has 2 coffee cups arrangement can be done in three ways.
Total arrangements for case 2=1×3×3×3=27
So, total arrangement for given conditions =54+27=81.