In how many different ways can the letters of the word 'DELETE' be arranged?

120

The correct answer is Option (4) → 120

1. Count the Total Letters

The word 'DELETE' has 6 letters in total ($n = 6$).

2. Identify Repeating Letters

Now, we count how many times each letter appears:

• D: 1 time
• E: 3 times
• L: 1 time
• T: 1 time

The letter 'E' is the only one that repeats, appearing 3 times.

3. Apply the Permutation Formula

The formula for the number of arrangements is:

$\frac{n!}{p! \cdot q! \dots}$

Where $n!$ is the factorial of the total number of letters, and $p!, q!$, etc., are the factorials of the counts of repeating letters.

$\text{Arrangements} = \frac{6!}{3!}$

4. Solve the Calculation

• $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$
• $3! = 3 \times 2 \times 1 = 6$

$\frac{720}{6} = 120$

Conclusion

The letters of the word 'DELETE' can be arranged in 120 different ways.