A selection is to be made for one post of Principal and two posts of Vice-Principal. Amongst the six candidates called for the interview, only two are eligible for the post of Principal while they all are eligible for the post of Vice-Principal. The number of possible combinations of selectees is

The correct option is None of the above.

Let us break down the selection process step-by-step to find the total number of possible combinations of selectees.

We need to select:
- 1 candidate for the post of Principal
- 2 candidates for the posts of Vice-Principal
There are 6 candidates in total. Let us denote them as candidates.
Only 2 specific candidates (let's call them A and B) are eligible for the post of Principal.
All 6 candidates are eligible for the post of Vice-Principal.

Since the eligibility for the post of Principal is restricted to only 2 candidates, we must analyze the selection based on who is selected as the Principal. A candidate cannot hold both the Principal and Vice-Principal posts simultaneously.

Case 1: Candidate A is selected as the Principal.
If Candidate A is chosen as Principal, A is no longer available for the Vice-Principal posts.
This leaves 5 remaining candidates (Candidate B and the other 4 candidates) eligible for the 2 Vice-Principal posts.
The number of ways to choose 2 Vice-Principals from these 5 candidates is given by the combination formula:
$${}_{5}C_2=\frac{5\times 4}{2\times 1}=10$$
So, there are 10 combinations in this case.

Case 2: Candidate B is selected as the Principal.
If Candidate B is chosen as Principal, B is no longer available for the Vice-Principal posts.
This leaves 5 remaining candidates (Candidate A and the other 4 candidates) eligible for the 2 Vice-Principal posts.
Similarly, the number of ways to choose 2 Vice-Principals from these 5 candidates is:
$${}_{5}C_2=10$$
So, there are 10 combinations in this case.

Total Number of Combinations:
Adding the combinations from both mutually exclusive cases:
$$\text{Total combinations}=10+10=20$$

Since the actual number of possible combinations is 20, and this value is not present in the options (4, 12, or 18), the correct option is indeed None of the above.