Every pair of links in a mechanism, whether they physically touch each other or not, has one instantaneous centre associated with it, because Kennedy's theorem treats every possible pair of links, including the fixed one, as sharing a common point of zero relative velocity at that instant. So the total count is simply the number of ways to pick 2 links out of the total, which for 5 links is \( \binom{5}{2} = \dfrac{5 \times 4}{2} = 10 \), matching option (A).