Question

determine whether the statement below is true or false. if it is false, rewrite it as a true statement.

a combination is an ordered arrangement of objects.

choose the correct answer below.

a. the statement is false. a true statement would be \a combination is a distinguishable arrangement of objects.\
b. the statement is true.
c. the statement is false. a true statement would be \a permutation is an ordered arrangement of objects.\
d. the statement is false. a true statement would be \a combination is an ordered arrangement of permutations.\

Explanation:

Analyze the given statement

Using the Combinatorics knowledge point
The statement is: "A combination is an ordered arrangement of objects."

Evaluate the definition of a combination

Using the Combinatorics knowledge point
A combination is a selection of items where the order does not matter. Therefore, the given statement is false.

Identify the correct definition of an ordered arrangement

Using the Combinatorics knowledge point
An ordered arrangement of objects is called a permutation. Thus, a true statement is: "A permutation is an ordered arrangement of objects."

Match with the given options

Using the Combinatorics knowledge point

• Option A suggests a combination is a distinguishable arrangement, which does not address order.
• Option B states the original statement is true, which is incorrect.
• Option C correctly identifies the statement as false and provides the correct definition of a permutation.
• Option D suggests a combination is an ordered arrangement of permutations, which is incorrect.

Answer:

• A. The statement is false. A true statement would be "A combination is a distinguishable arrangement of objects."
• B. The statement is true.
• C. The statement is false. A true statement would be "A permutation is an ordered arrangement of objects." (Correct answer)
• D. The statement is false. A true statement would be "A combination is an ordered arrangement of permutations."