First remove:
Probability of removing a trained rat is 6/8
Probability of removing untrained rat is 2/8
Outcome is 6/8 + 2/8 = 1
Second remove:
Probability of picking a trained rat is 5/7
Probability of picking untrained rat is 1/7
Outcome is 6/7
Third remove:
Outcome is 1 (Since you can only remove a trained rat)
Forth remove:
Outcome is 1 (Since you can only remove a trained rat)
Fifth remove:
Outcome is 1 (Since you can only remove a trained rat)
Total outcome = 1 + 6/7 + 1 + 1 + 1 = 34/7 = 4(6/7)