A captain and a co-captain are randomly selected from the 12 members of a fencing team. Determine the probability that Lauren is chosen as the captain, and Isabel is chosen as the co-captain

there is one way to choose Lauren as captain and Isabel as co-captain. there are 12 choose 2 ways (permutations) to choose a captain and co-captain , (since order counts)
so the answer is 1 / 12 P2

for the denominator, there are 12 ways to choose captain, and for each of these choices there are 11 remaining for co-captain , so 12 x 11 total ways to choose captain and co-captain