It’s the time of year for Sports Day, and in each tutor group, every student must sign up either to run, or to jump, or to throw for the tutor group team.

In one particular tutor group there are 15 students, including one pair of twins and one set of triplets. As nobody in this group remembers to sign up before Sports Day, the tutor allocates, at random, five students to running, five to jumping and five to throwing.

What is the probability that the twins end up doing the same activity but that the triplets are all doing something different?