Employees of Each Department

What was the data given? 

Let's make a table where columns represent the sport & row represents the employee.There are 3 tables 1 for each department. To make table shorter we will use the initials only of sports' & employees' names as below.

Table

A - Alex, B - Betty, C - Carol, D - Dan, E - Earl, F - Fay, G - George, H - Harry. 

F - Football, C - Cricket, V - Volleyball, Bd - Badminton, LT - Lawn Tennis, Bs - Basketball,
H - Hockey, TT - Table Tennis  

Now taking clues one by one into consideration.

1. Dan works in Administration and does not like either Football or Cricket.

Table 1

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2. Fay works in Personnel with only Alex who likes Table Tennis.

This indicates that Alex is working in Personnel department & likes Table Tennis. Fay working in same department may like any other sports than Table Tennis. No body other working in this department.

Table 2

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3. Earl and Harry do not work in the same department as Dan.

Hence they must be working in Marketing department!

Table 3

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4. Carol likes Hockey and does not work in Marketing.

That's why his department must be Administration.

Table 4

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5. George does not work in Administration and does not like either Cricket or Badminton.

His department must be Marketing & he might be liking Football or Volleyball or Lawn Tennis or Basketball.

Table 5

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6. One of those who work in Administration likes Football.

The table from 5th clue clearly indicates that the person at which this clue pointing is Batty.

Table 6

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7. The one who likes Volleyball works in Personnel.   

Obviously, this person is Fay. Remember clue 1, there are only 2 persons in Personnel viz. Alex & Fay. Alex likes Table Tennis hence Fay must be liking Volleyball.

Table 7

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8. None of those who works in Administration likes either Badminton or Lawn Tennis.

Table 7 shows that Batty, Carol & Dan working in this department. Since Batty like Football & Carol likes Hockey, the given clue indicates Dan must be fan of Basketball.

Table 8

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9. Harry does not like Cricket.

If he doesn't like cricket then Earl must be liking Cricket.

Table 9

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The table leaves only option of sports for George and that is Lawn Tennis.

Table 10

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 Now we have complete picture of each employee's department & his favorite sport.
So let's turn to the question asked.

1.Who are the employees who work in the Administration Department?

Batty, Carol & Dan are working in the Administration Department.

2. In which Department does Earl work?

The Marketing Department.