IMO 1984 LL SWE57

Let a, b, c, d be a permutation of the numbers 1, 9, 8, 4 and let

IMO 1984 LL SWE57

Origin: SWE

Problem

Let a, b, c, d be a permutation of the numbers 1, 9, 8, 4 and let n = (10a + b)10c+d. Find the probability that 1984! is divisible by n.