- Arrangement: n items can be arranged in n! ways
- Permutation: A way of selecting and arranging r objects out of a set of n objects: $$ ^{n}\textrm{P}_{r}$$ = $$\frac{n!}{(n-r)!}$$
- Combination: A way of selecting r objects out of n (arrangement does not matter) $$ ^{n}\textrm{C}_{r}$$ = $$\frac{n!}{r!(n-r)!}$$
- Selecting r objects out of n is same as selecting (n-r) objects out of n $$^{n}C_{r}$$ = $$^{n}C_{n-r}$$
- Also, one will note, $$^{n}\textrm{C}_{r} \times r!= ^{n}\textrm{P}_{r}$$
- $$\sum_{k=0}^{n}$$ $$^{n}C_{k}=2^{n}$$
- nCr + nC(r-1) = (n+1)Cr
- nC0 = nCn = 1
