How many five-letter words are there?

Understand the Problem

The question is asking for the total number of possible five-letter words that can be formed, which involves calculating permutations or combinations of letters.

Answer

11,881,376
Answer for screen readers

The total number of possible five-letter words is 11,881,376

Steps to Solve

  1. Determine the total number of letters in the alphabet

The English alphabet has 26 letters.

  1. Consider each position in the five-letter word

Each of the five positions in the word can be filled by any of the 26 letters.

  1. Calculate the total number of permutations

Since the choice of letters is independent for each position, the total number of five-letter words is given by the product of the number of choices for each position:

$$ 26 \times 26 \times 26 \times 26 \times 26 = 26^5 $$

  1. Perform the exponentiation

Now compute the value of $26^5$:

$$ 26^5 = 26 \times 26 \times 26 \times 26 \times 26 = 11,881,376 $$

The total number of possible five-letter words is 11,881,376

More Information

This includes any combination of letters, whether they form real words or not.

Tips

A common mistake is to fail to recognize that the order in which the letters are placed matters in the creation of a word, necessitating the use of permutations rather than combinations.

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