When arranging n objects where p are identical of type 1, q identical of type 2, etc., the number of distinct arrangements = n!/(p! * q! * ...). Classic example: MISSISSIPPI has 11 letters (M:1, I:4, S:4, P:2), arrangements = 11!/(4! * 4! * 2!) = 34650. Always identify and count repeated elements first before applying the formula.