You arrange the digits 1, 2, 3, 4, 5, 6 at random. What is the probability that you get a multiple of 12?
In order to arrange them as multiples of 12, the 6 digits must end in one of the following combinations in order to be divisible by 12:
12, 16, 24, 32, 36, 52, 56, 64 = 8 arrangements.
The other 4 digits can be arranged in 4! = 24 ways.
Therefore, you will have: 8 x 24 = 192 arrangements as multiples of 12 out of a total of 6! = 720 total arrangements.
The pobabability is: 192 / 720 =4 /15
