How many 8-digit numbers made from which is divisible by and its digits are distinct?
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The number must be a multiple of 9999.If the number is in the form of a b c d e f g h ,then a b c d + e f g h = 9 9 9 9 ,we get a + e = b + f = c + g = d + h = 9 We know 1 + 8 = 2 + 7 = 3 + 6 = 4 + 5 = 9 ,so we'll have to find the possibilities of a b c d .
a has 8 possibilities, b has 6, c has 4, d has 2.So it's 8 × 6 × 4 × 2 = 3 8 4