Question

select the correct answer from each drop-down menu.
determine whether each situation describes a permutation or a combination.

situation	permutation or combination?
the swim team must choose a captain and co - captain.	\\(\square\\)
a sandwich made with 3 of the 25 available toppings.	\\(\square\\)
a locker has a 5 - digit code that must be entered to open it.	\\(\square\\)

Explanation:

To determine if a situation is a permutation or combination, we use the key difference: permutations care about order (arrangements), combinations do not (selections).

1. The Junior class elects 3 representatives to the student council.

When electing representatives, the order in which students are chosen does not matter (e.g., choosing Alice, Bob, Charlie is the same as Bob, Alice, Charlie for the role of "representative"). This is a combination.

2. The swim team must choose a captain and co - captain.

Here, order matters: choosing Alice as captain and Bob as co - captain is different from Bob as captain and Alice as co - captain. This is a permutation.

3. A sandwich made with 3 of the 25 available toppings.

The order of the toppings on the sandwich does not matter (e.g., lettuce, tomato, onion is the same as tomato, lettuce, onion for the sandwich). This is a combination.

4. A locker has a 5 - digit code that must be entered to open it.

The order of the digits in the code matters (e.g., 12345 is a different code than 54321). This is a permutation.

Answer:

• 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