How many words, with or without meanings, can be formed using all the letters of the word 'EQUAL', using each letter exactly once ?

Options

A. `5!`
B. `5(5!)`
C. `24`
D. None

Answer

To find the total number of words that can be formed using all the letters of the word 'EQUAL', we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Letters**: The word 'EQUAL' consists of 5 letters: E, Q, U, A, L.

2. **Check for Distinct Letters**: All the letters in 'EQUAL' are distinct. This is important because if there were any repeated letters, the calculation would change.

3. **Calculate the Total Arrangements**: Since all the letters are different, the total number of arrangements (or permutations) of these letters can be calculated using the factorial of the number of letters.

The formula for permutations of n distinct objects is given by:
\[ n! = n \times (n-1) \times (n-2) \times \ldots \times 1 \]

Here, \( n = 5 \) (the number of letters in 'EQUAL').

4. **Compute the Factorial**:
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 \]
- Calculate step-by-step:
- \( 5 \times 4 = 20 \)
- \( 20 \times 3 = 60 \)
- \( 60 \times 2 = 120 \)
- \( 120 \times 1 = 120 \)

5. **Conclusion**: Therefore, the total number of words that can be formed using all the letters of the word 'EQUAL' is \( 120 \).

### Final Answer:
The total number of words that can be formed is **120**.

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