Method-2

Let department members are: A, B, C, D, and E and A and B refuse to attend the conference together.

Hence, Total cases in which we A and B can be there in a pair:

• Both A and B are in the pair OR

• A is in the pair and B is not in the pair

• B is in the pair and A is not in the pair

• Neither of A or B is in the pair.

But,

out of all the cases we are not selecting 1 case:- When both A and B are in the pair.Thus, if we remove the case when both A and B are in the pair from the total pairs, we will get the answer.

• Total Pairs: \(^5c_2\)

• Total Pairs when both A and B are in the pair= 1

Thus, required answer= 10-1

Hence, total ways=9

Hence, the correct answer is option B.

Answer: B
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