In how many ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin?

For $$1 \leq r \leq n, \frac{1}{r+1}\left\{{ }^n P_{r+1}-{ }^{(n-1)} P_{r+1}\right\}$$ is equal to

In how many ways 4 balls can be picked from 6 black and 4 green coloured balls such that at least one black ball is selected?

In how many ways can 9 examination papers be arranged so, that the best and the worst papers are never together?