Question

determine if the outcome of the event described would be found using a permutation or a combination.
placing items in a line
choosing cards from a deck of cards
choosing a committee of 5 people
placing first or second in a race
choosing 3 - digit lock combinations
permutation
combination

Explanation:

To solve this, we recall:

• Permutation: Order matters (arrangements, rankings, sequences).
• Combination: Order does not matter (selections, groups where order is irrelevant).

1. Placing items in a line

Order of items in the line matters (e.g., item A first vs. item B first is different).
Classification: Permutation

2. Choosing cards from a deck

When choosing cards (e.g., 5 - card hand), the order of drawing does not matter (a hand with Ace - King is the same as King - Ace).
Classification: Combination

3. Choosing a committee of 5 people

A committee’s membership is about selection, not order (Person A, B, C is the same as Person C, B, A in the committee).
Classification: Combination

4. Placing first or second in a race

Order matters (1st place vs. 2nd place is a distinct outcome).
Classification: Permutation

5. Choosing 3 - digit lock combinations

The order of digits in a lock matters (e.g., 1 - 2 - 3 vs. 3 - 2 - 1 are different combinations).
Classification: Permutation

Final Grouping:

• Permutation: placing items in a line, placing first or second in a race, choosing 3 - digit lock combinations
• Combination: choosing cards from a deck of cards, choosing a committee of 5 people

Answer:

(Grouped):

• Permutation: placing items in a line, placing first or second in a race, choosing 3 - digit lock combinations
• Combination: choosing cards from a deck of cards, choosing a committee of 5 people