The Fundamental Counting Principle

≈ 25 min

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The Fundamental Counting Principle

If a process has successive independent choice stages with $m,n,\ldots$ options, the total number of outcomes is their product. Restrictions change the number of choices at affected stages.

Worked reasoning

There are 26 choices for each letter and 10 for each digit.
Multiply $26^2\times10^3$ .
The total is $676000$ .

Key idea

Multiply the number of legal choices at each successive stage.

A code has two letters followed by three digits. Repetition is allowed. How many codes are possible?

Which statement best captures the central mathematical idea in The Fundamental Counting Principle?

Multiply the number of legal choices at each successive stage.

Counts from successive choice stages should always be added.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about The Fundamental Counting Principle, which move is most reliable?

Define the stages and apply restrictions before multiplying.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with The Fundamental Counting Principle?

Counts from successive choice stages should always be added.

Multiply the number of legal choices at each successive stage.

Define the stages and apply restrictions before multiplying.

Test a smaller version by listing outcomes and compare with the product.