Let k be a positive integer. Suppose that the integers 1, 2, 3, ...3k, 3k + 1 are written down in random order.

What is the probability that at no time during this process, the sum of the integers that have been written up to that time is divisible by 3?

Source: Putnam competition

(In reply to

re(4): Solution by Charlie)

Thanks Charlie.

After another look, I found my mistake was actually one line earlier. I wrote ((3k)!)P(k!) = (3k)!/((2k)!*k!), the combination formula instead of ((3k)!)P(k!) = (3k)!/(2k)!, the permutation formula.