Explanation:

- The holidays are on either the 2nd or 5th of October, November, and December.

- M and K: three people holiday between them, with M after K.

- H immediately follows L.

- Two people holiday between J and M.

- I doesn't holiday in December.

Starting with M and K logic:

- If K goes in October, M would be in December.

- People between them are possible if K is on Oct 2, M is on Dec 2 or K is on Oct 5, M is on Dec 5.

Other constraints:

- H immediately after L, so they take consecutive slots.

- With I not in December, consider I’s placement in October or November.

Resolving with specific dates:

1. K on Oct 2

2. J on Oct 5

3. L and H on Nov 2 and Nov 5 (respectively)

4. I on Dec 2

5. M on Dec 5

With I on Dec 2, K follows immediately on Dec 5.

- K goes after I.

Hence:

Option: 2, K is the correct answer.