Explanation:

Correct Answer is (a).The given sentence explains that it is not required to mention in the office that only three winners will get a trip to Europe under the competition.
Now, if we look at the bold parts of the sentence, If need is followed by not, it turns into a modal auxiliary and you cannot use needs in that context. Hence, it is wrong to use needs not mention in the first part of the sentence. In the second part given in bold, it is observed that both the ordinal and cardinal numbers are in use i.e. both three and first are there. In such a scenario, the ordinal should always precede the cardinal number used. So, first three lucky winners would have been the correct usage.
The correct sentence would be: He need not mention in the office that only the first three lucky winners will win a trip to Europe.This makes option A the correct choice among the given options.