Question

determine whether the object is a permutation or a combination.
the batting order for a baseball team

choose the correct answer below.
a. this is a combination because repetition is not allowed and the order of the items does not matter.
b. this is a permutation because repetition is not allowed and the order of the items matters.
c. this is neither a permutation nor a combination because repetition is allowed.
d. there is not enough information given to make a decision.

Explanation:

Step1: Recall Permutation/Combination

Permutation: order matters, no repetition. Combination: order doesn't matter, no repetition.

Step2: Analyze Batting Order

Batting order: each player bats once (no repetition), and the order (who bats 1st, 2nd, etc.) matters. So it's a permutation.

Step3: Evaluate Options

• A: Wrong (order matters in batting order).
• B: Correct (no repetition, order matters).
• C: Wrong (no repetition in batting order).
• D: Wrong (enough info: order and no repetition).

Answer:

B. This is a permutation because repetition is not allowed and the order of the items matters.