How many three-letter “words” (strings of letters) can be formed using the 26 letters of the alp

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How many three-letter “words” (strings of letters) can be...

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Key Concepts

Fundamental Counting Principle

This principle states that if there are several independent tasks to be performed, and there are a certain number of ways each task can be completed, then the total number of ways to complete all tasks is the product of the number of ways each individual task can be done. In the context of forming words, each letter position represents an independent task, and the ways to assign a letter to each position multiply together to yield the total number of words.

Counting with Replacement

When repetition is allowed, each position in the sequence can be filled by any of the available letters, regardless of what was chosen in previous positions. This results in a scenario where the number of choices remains constant for each position, leading to calculations that involve a constant number of options for every choice slot.

Counting without Replacement (Permutations)

When repetition is not allowed, once a letter is used in one position, it cannot be used again in another position. This alters the number of choices available for subsequent positions. This is a specific type of permutation problem where order matters and the choices decrease as letters are used.

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