Question

answer the following question using the appropriate counting technique, which may be either arrangements with repetition, permutations, or combinations. be sure to explain why this counting technique applies to the problem.
how many license plates can be made of the form xxxx-yy, where x is a letter of the alphabet and y is a numeral 0-9?

what counting technique should be used to make this calculation?
a. arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated.
b. arrangements with repetitions because the selections come from a single group of items, and the order of the arrangement matters.
c. combinations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement does not matter.
d. permutations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement matters.

how many license plates can be made of the form xxxx-yy, where x is a letter of the alphabet and y is a numeral 0-9?
a. there are 3,276,000 possible license plates.
b. there are 45,697,600 possible license plates.
c. there are 6,760,000 possible license plates.
d. there are 32,292,000 possible license plates.

Explanation:

Identify the counting technique

Using the Arrangements with Repetitions knowledge point

• The license plate format is XXXX-YY.
• Each X represents a letter of the alphabet (26 choices), and each Y represents a numeral 0-9 (10 choices).
• Since letters and digits can be repeated, and the order of the characters matters, this is a case of arrangements with repetitions.
• Therefore, the correct technique is arrangements with repetitions because there are \(r\) selections from a group of \(n\) choices and choices can be repeated.

Calculate the number of license plates

Using the Fundamental Counting Principle knowledge point

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Answer:

Question 1

• (A) Arrangements with repetitions because there are r selections from a group of n choices and choices can be repeated. (Correct answer)
• (B) Arrangements with repetitions because the selections come from a single group of items, and the order of the arrangement matters.
• (C) Combinations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement does not matter.
• (D) Permutations because the selections come from a single group of items, no item can be selected more than once and the order of the arrangement matters.

Question 2

• (A) There are 3,276,000 possible license plates.
• (B) There are 45,697,600 possible license plates. (Correct answer)
• (C) There are 6,760,000 possible license plates.
• (D) There are 32,292,000 possible license plates.