Consider a relation schema r(A, B, C, D, E, F) and attribute A is element of every candidate key of r. Maximum number of possible candidate keys of r is ________.

Maximum number of candidate keys for a relation can be given by:$\binom{n}{\left \lceil n/2 \right \rceil}$. For example R(A,B,C,D) have AB,BC,CD,AD,BD .Here A is fixed in any candidate key, so for other 5 attributes we have $\binom{5}{\left \lceil 5/2 \right \rceil} = 10$ keys. So, answer is 10.