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.

calculate how many different passwords are possible.
(type a whole number.)

Explanation:

Identify the counting technique

Using the Permutations knowledge point

• The problem asks for six-character passwords from letters A to F (6 letters) without repetition.
• Since repetition is not allowed, each letter is used exactly once.
• The order of characters in a password matters.
• Therefore, permutations apply because no item is selected more than once and order matters.

Calculate the number of passwords

Using the Permutations knowledge point

$$ P(6, 6) = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 $$

Answer:

Question 1

• 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.

Question 2

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