A signboard painter has to repaint the nine letters of the word ALLAHABAD in some order. How many different nine-letter strings could he end up painting?

ALLAHABAD has 9 letters: A appears four times, L twice, and H, B, D once each. Distinct arrangements = 9!/(4! × 2!) = 362880/48 = 7560. Trap 15120 = 9!/4! handles the four A's but overlooks the repeated L. Trap 30240 = 9!/(3! × 2!) miscounts the A's as three instead of four. Trap 362880 = 9! treats every letter as different, which would only be right if the repeats were labelled apart.