How many runs score?

[DaveASA/FED]

Maybe I lost it but you said that a force could not be made if the BR gets thrown out. I agree in this case as the outs did not occur in the correct order that R1's run would score. But what if there is one out bases loaded and a long shot to the outfield and BR get thrown out at the plate for the second out of the inning. Then the smart catcher appeals that R1(from 3rd) did not touch home plate when she ran in. You agree and ring her up for the 3rd out of the inning. If I remember correctly that would be the third out and since R1 was forced to advance and this was the 3rd out then all runs would be cancelled. I base this on the forth out appeal rule that if I remember correctly is the same situation I described above except there were two outs and the BR was the 3rd, and you appeal for the 4th out so you can eliminate the runs scored. What am I missing?