Let's determine whether each situation describes a permutation or a combination by analyzing if the order of selection matters or not.
1. The Junior class elects 3 representatives to the student council.
In this situation, the order in which the representatives are chosen does not matter. What matters is who is chosen, not the sequence in which they are chosen.
- Answer: Combination
2. The swim team must choose a captain and co-captain.
Here, the order matters because a captain and a co-captain have different responsibilities and roles. Choosing Alice as captain and Bob as co-captain is different from choosing Bob as captain and Alice as co-captain.
- Answer: Permutation
3. A sandwich made with 3 of the 25 available toppings.
For the sandwich, the order of toppings does not matter. The focus is on which toppings are selected, regardless of the order in which they are added.
- Answer: Combination
4. A locker has a 5-digit code that must be entered to open it.
The order of the digits in the code is crucial because a specific sequence is required to open the locker. Entering the correct digits in the wrong order would not work.
- Answer: Permutation
In summary, the answers are:
- The Junior class elects 3 representatives to the student council: Combination
- The swim team must choose a captain and co-captain: Permutation
- A sandwich made with 3 of the 25 available toppings: Combination
- A locker has a 5-digit code that must be entered to open it: Permutation
