this is a question about Katz-Lindell book, introduction to modern cryptography, 2nd edition, exercise 4.7, part c.

For a) and b) it is clear that the Macs are insecure, but for c) I am struggling to see why. For me, when the attacker will present his pair (m*, <r*,t*>), the Mac will sample uniformly its own r (before applying the Vrfyk(.) algorithm), and will prepend r to the computed t. So no matter how the attacker will choose m* (even if the attacker chooses m* randomly), the Mac (assuming that it is a deterministic Mac using a canonical verification) will always sample a random r from {0,1}power n, independently from the one (r*) that the attacker output to it, and the probability that r=r* will be negligible. So it is still secure Mac, the one presented in part c). Can someone correct me if I am wrong please? Thank you