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

120

The correct answer is Option (2) → 120

1. Analyze the word

First, count the total number of letters and identify any repeating letters:

• Total number of letters (n): 6 (D, E, L, E, T, E)
• Repetitions: The letter 'E' appears 3 times.
• All other letters (D, L, T) appear only once.

2. The Formula

The number of distinct arrangements of $n$ objects where $p$ objects are of one type, $q$ of another, and so on, is:

$\text{Arrangements} = \frac{n!}{p! \cdot q! \dots}$

3. Calculation

Substitute our values into the formula:

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

Now, calculate the factorials:

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

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

Correct Option: 120