# Q. There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee?

a. 18

b. 27

c. 54

d. 81

Correct Answer: d. 81

#### Question from UPSC Prelims 2022 CSAT Paper

**Explanation : **

## There are 9 cups placed on a table

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.

Hence, the correct answer is an option(4) i.e., 81.