Probability - Permutations and Combinations

Permitations: $^nP_m$
Combinations : $^nC_m$
Whole numbers : n, m

1. Factorial
$n!=1.2.3...(n-2)(n-1)n$
$0!=1$
2. $^nP_n=n!$
3. $^nP_m={n! \over (n-m)!}$
4. Binomial Coefficient
$^nC_m=\Bigg( {\substack{n\\ \\ \\ \\\\\\\\\\\\\\m}}\Bigg)= {n! \over m!(n-m)!}$
5. $^nC_m=^nC_{n-m}$
6. $^nC_m+ ^nC_{m+1}= ^{n+1}C_{m+1}$
7. $^nC_0+ ^nC_1+^nC_2+...+^nC_n= 2^n$
8. Pascal's Triangle