Question

alberta diploma question
a new licence plate in alberta consists of three letters followed by four digits. letters are chosen from a list of 19 acceptable letters that may be repeated. maureen wants the first letter on her licence plate to be an m, which is an acceptable letter, and she also wants the four digits to match the last four digits of her cell phone number in the same order.
the number of licence plates that will meet maureen’s criteria is

Explanation:

Step1: Analyze the first - letter condition

The first letter is fixed as 'M', so there is 1 way to choose the first letter.

Step2: Analyze the second - letter condition

There are 19 acceptable letters and the second letter can be any of them, so there are 19 ways to choose the second letter.

Step3: Analyze the third - letter condition

Similarly, there are 19 ways to choose the third letter as letters can be repeated and there are 19 acceptable letters.

Step4: Analyze the digit condition

The four - digit part is fixed to match the last four digits of her cell - phone number in the same order, so there is 1 way to choose the four digits.

Step5: Calculate the total number of license plates

By the counting principle, the total number of license plates that meet the criteria is the product of the number of ways to choose each part. So the total number is \(1\times19\times19\times1 = 361\).

Answer:

361