The total number of permutations of $$n$$ different things taken not more than $$r$$ at a time, when each thing may be repeated any number of times is

How many chords can be drawn through 21 points on a circle?

If a polygon of $$n$$ sides has 560 diagonals, then $$n=$$

A person writes letters to 6 friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes? Notation $$D_n=n!\left(\sum_\limits{i=0}^n \frac{(-1)^i}{i!}\right)$$