Solution:
Let the sequence of consecutive integers begins with the integer m. Then, the consecutive integers are
Out of these integers, 3 integers can be chosen in ways.
Let us divide these consecutive integers into three groups
and as follows:
The sum of 3 integers chosen from the given 3n integers will be divisible by 3 if either all the three integers are chosen from the same group or one integer is chosen from each group. The number of ways that the three integers are from the same
group is and the number of ways that the
integers are from different groups is
So, the number of ways in which the sum of three integers is divisible by 3 is
Hence, required probability