If the six digits 1, 2, 3, 5, 5, and 8 are randomly arranged into a six-digit positive integer, what is the probability that the integer is divisible by 14? Express your answer as a common fraction.
1, 2, 3, 5, 5, 8 ==6! / 2! ==360 permutations.
2^4==16 - permutations are divisible by 14 as follows:
(125538, 153258, 235158, 251538, 255318, 351582, 358512, 512358, 515382, 518532, 531258, 532518, 553182, 553812, 581532, 585312) >>Total = 16
Therefore, the probability is: 16 / 360 ==2 / 45
