Binomial Theorem - Binomial Coefficients and Pascal's Triangle

Binomial Theorem - Binomial Coefficients and Pascal's Triangle

IP 4

Evaluate the following without using a calculator

  1. \(\binom{10}{3}\)
  2. \(\binom{n+2}{2}\) in terms of \(n\)
  3. \(\binom{n+1}{n}\) in terms of \(n\)
  4. \(\binom{n}{n}\) in terms of \(n\)

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Answer:(a) \(120\) (b) \(\frac{(n+2)(n+1)}{2}\) (c) \(n+1\) (d) \(1\)

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