So after reading this... I reviewed what I studied in statistics and I still not sure if I remember it right... But I think all of those who commented before me are wrong.

There are 3 items (x,y.z), each one of them can have one of 3 events (A, B, C). the order is important. So there are 27 outcomes for this problem.

But 3 of the outcomes fit the citera "all three management trainees apply for the same quarter" that is in the three events AAA, BBB, CCC. so we have a probabilty of 3/27 = %11.111.

My solution is: %11.111