Question

answer the following question using arrangements with repetition, permutations, or combinations. be sure to explain why the particular counting technique applies to the problem.

how many different six-character passwords can be formed from the uppercase letters a to f if repetition is not allowed?

determine the appropriate counting technique. choose the correct answer below.

a. permutations should be used because we make selections from a group of choices.
b. arrangements with repetition should be used because no item may be selected more than once and the order matters.
c. permutations should be used because no item may be selected more than once and the order matters.
d. arrangements with repetition should be used because we make selections from a group of choices.
e. combinations, because no item may be selected more than once and the order does not matter.

Explanation:

Analyze the problem constraints

Using the Permutations, Combinations, and Arrangements with Repetitions knowledge points

• We need to form a six-character password from the uppercase letters A to F.
• The letters A to F represent exactly 6 distinct items.
• Repetition is not allowed.
• Since we are forming a password, the order of characters matters.

Evaluate the counting techniques

Using the Permutations and Combinations knowledge points

• Combinations are used when order does not matter.
• Arrangements with repetitions are used when items can be selected more than once.
• Permutations are used when order matters and repetition is not allowed.

Match with the correct option

Using the Permutations knowledge point

• The correct technique is permutations because no item may be selected more than once and the order matters.
• This matches option C.

Answer:

• A. Permutations should be used because we make selections from a group of choices.
• B. Arrangements with repetition should be used because no item may be selected more than once and the order matters.
• C. Permutations should be used because no item may be selected more than once and the order matters. (Correct answer)
• D. Arrangements with repetition should be used because we make selections from a group of choices.
• E. Combinations, because no item may be selected more than once and the order does not matter.