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

The correct answer is Option (4) → 1260

ARRANGE has 7 letters, in which A comes twice and R comes twice. Swapping the two A’s, or the two R’s, gives the same word, so \(7!\) is divided by \(2!\) for each repeated letter.

• Number of arrangements \(\displaystyle =\frac{7!}{2!\times2!}=\frac{5040}{4}=1260\)