There are only three tasks and 5 people. The number of ways of selecting 3 out of 5 people to perform these tasks is also the number of ways of (de-)selecting 2 out of 5, which is 10. Having selected the people we now have to work out who does what. There are 6 ways of arranging 3 tasks. The selected people can be assigned their tasks in 6 ways, so in total there are 6*10=60 ways of selecting and organising 3 out of 5 people to carry out three tasks.
To show this as a tree diagram, the first set of branches will be all the ways of selecting the people (shown by their initial letters):
We need three main branches to start with: V, L, M;
on the V main branch we have 3 sub-branches: L, M, H;
on the V-L sub-branch we have 3 twigs: M, H, R;
on the V-M sub-branch we have 2 twigs: H, R;
on the V-H sub-branch we put twig R.
On the L main branch we have 2 sub-branches: M, H;
on the L-M sub-branch we have 2 twigs: H, R;
on the L-H sub-branch we have twig R.
On the M main branch we have one sub-branch H and one twig R on that branch.
This arrangements gives us 10 twigs, corresponding to the 10 combinations of people. I've taken the people in order of appearance: V, L, M, H, R, but that was arbitrary. We could have chosen any order, and we would still have ended up with 10 twigs. The main branch V involves L, M, H, R, those people further "along the line" so to speak. L involves M, H, R; so it's only necessary to involve people further down the line, because, for example, the combinations involving V and M have already been covered by the main branch V.
Each person in the group of three can be assigned one of three tasks; that leaves 2 tasks for the remaining two people. There are two ways two people can be assigned two tasks, so there are 3*2=6 ways for three people to be assigned three tasks. We can attach these 6 ways: b for beverage, f for food and i for invitations: bfi, bif, fbi, fib, ibf, ifb. These 6 are the leaves on each of the 10 twigs. By tracking along each branch, twig and leaf we have all 60 possible arrangements.
