Question

probability
counting principle with repetition allowed
a car company is going to issue new id codes to its employees. each code will have one digit followed by four letters. the letter v and the digits 3, 4, and 5 will
not be used. so, there are 25 letters and 7 digits that will be used. assume that the letters can be repeated. how many employee id codes can be generated?
employee id codes

Explanation:

Step1: Determine the number of choices for the digit

There are 7 choices for the digit part of the ID code.

Step2: Determine the number of choices for each letter

Since there are 25 letters and they can be repeated, for each of the 4 - letter positions, there are 25 choices.

Step3: Use the counting principle

By the counting principle (if there are \(m_1\) ways to do the first task, \(m_2\) ways to do the second task, \(\cdots\), \(m_n\) ways to do the \(n\)th task, then the total number of ways to do all \(n\) tasks together is \(m_1\times m_2\times\cdots\times m_n\)), the total number of ID codes is \(7\times25\times25\times25\times25\).

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Answer:

\(2734375\)