Questions: 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 permutation because repetition is not allowed and the order of the items matters. B. This is a combination because repetition is not allowed and the order of the items does not matter. C. This is neither a permutation nor a combination because repetition is allowed. D. There is not enough information given to make a decision.

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 permutation because repetition is not allowed and the order of the items matters.
B. This is a combination because repetition is not allowed and the order of the items does not matter.
C. This is neither a permutation nor a combination because repetition is allowed.
D. There is not enough information given to make a decision.

Transcript text: 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 permutation because repetition is not allowed and the order of the items matters. B. This is a combination because repetition is not allowed and the order of the items does not matter. C. This is neither a permutation nor a combination because repetition is allowed. D. There is not enough information given to make a decision.

Solution

Solution Steps

Step 1: Understand the problem

The question asks whether the batting order for a baseball team is a permutation or a combination. To determine this, we need to analyze whether the order of the items (players) matters and whether repetition is allowed.

Step 2: Analyze the characteristics of the batting order

Order matters: In a batting order, the sequence in which players bat is crucial. For example, Player A batting first and Player B batting second is different from Player B batting first and Player A batting second.
Repetition is not allowed: Each player can only appear once in the batting order. No player is repeated.

Step 3: Determine whether it is a permutation or a combination

A permutation is an arrangement of items where the order matters and repetition is not allowed.
A combination is a selection of items where the order does not matter and repetition is not allowed.

Since the batting order involves arranging players in a specific sequence (order matters) and no player is repeated (repetition is not allowed), it is a permutation.