57

Part of 1984 IMO Longlists

Problems(1)

Number formed by 1, 9, 8, 4 dividing 1984!

Source:

a, b, c, d

be a permutation of the numbers

1, 9, 8,4

n = (10a + b)^{10c+d}

. Find the probability that

1984!

is divisible by

n.

probabilitynumber theorycombinatorics unsolvedcombinatorics