B.2 Formulae And Notation

Formulae (Don’t Memorize!)

• \(^nC_r = {n! \over r!(n-r)!}\)
• \(^nC_r \times ^rP_r = ^nP_r = ^nP_r \times r!\) (Permutation-combination relationship)
• \(^{n+1}C_r = ^nC_r + ^nC_{r-1}\)
• \(^nC_r=?\) (from above, expanding twice up to n-2)
• \(^nC_r = ^nC_{n-r}\)

Notation

• \(^nC_r \equiv\) \(n \choose r\)
• Select 5 people from 6 \(\rightarrow ^6C_5 =\) \(6 \choose 5\)