Combination Formula

• \( \binom{n}{r} \) also written as \({}^{n} \mathrm{C} _r\), represents the number of ways to choose \(r\) items from \(n\) distinct items
  
• The order of selection does not matter

\(\binom{n}{r} = \frac{n!}{r! \times (n - r)!} = \frac{ n \times (n - 1) \times (n - 2) \times \dots \times (n - r + 1)}{r!}\)

• Useful identities:
  1. \( \binom{n}{0} = 1\)
  2. \( \binom{n}{1} = n\)
  3. \( \binom{n}{n-1} = n\)
  4. \( \binom{n}{n} = 1\)