Combinatorial numbers

Calculate the value of the following combinatorial numbers:

  1. $ \begin{pmatrix} 8 \\ 3 \end{pmatrix}$
  2. $ \begin{pmatrix} 4 \\ 1 \end{pmatrix}$
  3. $ \begin{pmatrix} 7 \\ 2 \end{pmatrix}$
  4. $ \begin{pmatrix} 157 \\ 0 \end{pmatrix}$

  1. $ \begin{pmatrix} 8 \ 3 \end{pmatrix}=\dfrac{8!}{3!\cdot(8-3)!}= \dfrac{8\cdot7\cdot6\cdot5!}{3!\cdot5!}=\dfrac{8\cdot7\cdot6}{3\cdot2}=56 $

  2. $ \begin{pmatrix} 4 \\ 1 \end{pmatrix}=4 $

  3. $ \begin{pmatrix} 7 \ 2 \end{pmatrix}=\dfrac{7!}{2!\cdot(7-2)!}= \dfrac{7\cdot6\cdot5!}{2!\cdot5!}=7\cdot3=21 $

  4. $ \begin{pmatrix} 157 \\ 0 \end{pmatrix}=1$

  1. $ 56 $

  2. $ 4 $

  3. $ 21 $

  4. $ 1$

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