What is the average (arithmetic mean) monthly salary, in...

What is the average (arithmetic mean) monthly salary, in dollars, for all the employees? To use a certain cash machine, you need a Personal Identification Code (PIC). If each PIC consists of two letters followed by one of the digits from 1 to 9$($ such as $\mathrm{AQ} 7$ or BB 3$)$ or one letter followed by two digits (such as $\mathrm{Q} 37$ or J88 ), how many different PICSs can be assigned?

What is the average (arithmetic mean) monthly salary, in dollars,
for all the employees?
To use a certain cash machine, you need a Personal Identification
Code (PIC). If each PIC consists of two letters followed by one of
the digits from 1 to 9$($ such as $\mathrm{AQ} 7$ or BB 3$)$ or one letter followed
by two digits (such as $\mathrm{Q} 37$ or J88 ), how many different PICSs can
be assigned?

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Key Concepts

Case Analysis in Counting Problems

Case analysis is a strategy used in combinatorial problems where the overall problem is divided into distinct, non-overlapping cases that are easier to manage. By calculating the number of outcomes for each case separately and then summing these counts, one can find the total number of outcomes for the problem.

Arithmetic Mean

The arithmetic mean is a statistical measure of central tendency, calculated by summing all the numerical values in a dataset and then dividing by the count of those values. It provides a single value that represents the average of the data, making it an essential concept in data analysis and statistics.

Multiplication Principle in Combinatorics

The multiplication principle is a foundational rule in combinatorics which states that if one event can occur in a certain number of ways and a second independent event can occur in another number of ways, then the total number of ways both events can occur in sequence is the product of the two numbers. This principle is key to solving problems that involve determining the number of possible outcomes for multi-step processes.

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