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

The word DELETE has 6 letters: D-E-L-E-T-E

Counting each letter:

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

The letter E repeats 3 times.

When letters repeat, the number of distinct arrangements is:

Number of arrangements = $\dfrac{6!}{3!}$

where $6!$ accounts for total letters and $3!$ accounts for the repetition of E.

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

$6! = 720$

$3! = 3 \times 2 \times 1$

$3! = 6$

Number of arrangements = $\dfrac{720}{6}$

Number of arrangements = $120$

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