Permutation and Combination

Permutation

• Number of ways in which we can arrange a set of things and Order is important

$$P(n,r) = {}^nP_r = {}_nP_r = \frac{n!}{(n - r)!}$$ where \(n\) is the number of objects to choose from and \(r\) is the number of objects actually selected to be arranged

Combination

• Number of ways in which we can arrange a set of things but Order is NOT important

\[ C(n,r) = {}^nC_r = {}_nC_r = \binom nr = \frac{n!}{r!(n - r)!} \]

Binomial Expansion

\[(q + p)^n = q^n + \binom n1 q^{n -1}p + \binom n2 q^{n - 2}p^2 + ... + p^n = \sum_{x=0}^n \binom nx p^xq^{n-x} \]