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

The word is DELETE: D-E-L-E-T-E

Total letters = 6 letters

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Count each letter:

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

The letter E repeats 3 times.

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When letters repeat, the formula for arrangements is:

$\text{Number of arrangements} = \frac{n!}{n_1! \times n_2! \times ...}$

Where $n$ is the total number of letters and $n_1, n_2...$ are the number of times each repeating letter appears.

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For the word DELETE:

$n = 6$ (total letters)

E repeats 3 times

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

$= \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1}$

$= \frac{720}{6}$

$= 120$

Therefore, the letters of DELETE can be arranged in 120 different ways.