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