Final answer:
The number of possible outcomes for selecting a captain and co-captain from the 12 students on the math league team is 12 choices for captain times 11 remaining choices for co-captain, which equals 132.
Step-by-step explanation:
To determine the number of possible outcomes for selecting a captain and a co-captain from 12 students on the math league team, we must use combination and permutation concepts. For the position of captain, any one of the 12 students can be chosen. Once a captain is elected, we have 11 remaining students to choose from for the position of co-captain. Since the captain and co-captain must be different individuals, this is a permutation problem because the order matters – being captain is not the same as being co-captain. The number of ways to choose the captain is simply 12. After a captain has been chosen, we have 11 options for choosing the co-captain. Hence, we can multiply the number of ways to pick a captain by the number of ways to pick a co-captain. This gives us a total of 12 x 11, which equals 132 possible outcomes for selecting a captain and a co-captain.