Personally, I didn't mind which Mouse with whom I would take a picture, because I was going to use it as one of my Christmas card pictures. As the 15 minutes ticked away, I saw Minnie Mouse approaching. But a Cast Member said to me as I was waiting, "Who would you prefer your picture with Mickey or Minnie?", and I said, "It doesn't matter, because I'm just happy to be here and get my picture with a Disney character!" She said, "Well, let's get you with Mickey," so they had Minnie wait to have Mickey take one last picture with me!
(This is my background and screen saver on my iPhone)