Study the given information carefully to answer the related questions:

Nine persons work in three departments i.e., operations, finance and marketing of a company. On their meeting day, they wear different color shirts i.e., white, blue, green, orange, red, black, purple, pink and violet. All the information is not necessary in the same order as given.

The persons work in operations do not wear orange and black. T works only with the one wearing green but not in marketing. R wears white and work with G but not in marketing. Only the persons wearing red and black work together in same department. B works with E and none of them wear black. A does not work in operations but wears violet. M neither works in finance nor with the one wearing red. The one wearing purple does not work in finance. G and D do not wear red and orange. H does not work with E who does not wear blue and orange.

How many persons work in finance department?

The correct answer is Five.

Let us analyze the given information step-by-step to determine the distribution of persons and shirt colors across the three departments: Operations, Finance, and Marketing.

Step 1: Department conditions and person groupings

There are 9 persons in total: T, R, G, B, E, A, M, H, D.

1. "T works only with the one wearing green but not in marketing."
Since T does not work in marketing, T must work in Operations or Finance. Since T works only with one person (who wears green), T's department has exactly 2 persons.

2. "Only the persons wearing red and black work together in same department."
This means another department also has exactly 2 persons, consisting strictly of the person wearing Red and the person wearing Black.

3. Since there are 9 persons in total and two departments contain exactly 2 persons each (2 + 2 = 4), the remaining department must contain 9 - 4 = 5 persons.
The three departments have sizes 2, 2, and 5.

Step 2: Assigning persons to departments

1. "R wears white and work with G but not in marketing."
R and G work together in Operations or Finance. Since the 2-person group with T is exclusive ("only with one wearing green"), R and G cannot be in T's group unless G is the one wearing green and T is only with G. But R works with G too, so G is in a group with at least two people (or part of the group of 5).

2. "A does not work in operations but wears violet."
3. "M neither works in finance nor with the one wearing red."
4. "B works with E and none of them wear black."

Let's find which department has 5 persons:
- The 2-person group #1: T and Green.
- The 2-person group #2: Red and Black.
- The 5-person group must be the remaining department, which is Finance (since T is not in Marketing, and both Operations and Marketing end up as the 2-person departments).

Thus, the number of persons working in the Finance department is 5 (while Operations and Marketing have 2 persons each).