The digits from 1 to 6 are arranged to form a six-digit multiple of 5. What is the probability that the number is greater than 500,000 and a multiple of 3? Express your answer as a common fraction.
There are 24 permutations which meet all your criteria: They are > 500,000 and multiples of 5 and multiples of 3 as follows:
(612345, 612435, 613245, 613425, 614235, 614325, 621345, 621435, 623145, 623415, 624135, 624315, 631245, 631425, 632145, 632415, 634125, 634215, 641235, 641325, 642135, 642315, 643125, 643215) >>Total = 24 such numbers.
The probability is: 24 / 6! ==24 / 720==1 / 30
