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
- Determine the total number of letters in the alphabet
The English alphabet has 26 letters.
- 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.
- 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:
$$ 26 \times 26 \times 26 \times 26 \times 26 = 26^5 $$
- 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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