# Problems from 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. $$\begin{pmatrix} 157 \\ 0 \end{pmatrix}$$
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### Development:

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

### Solution:

1. $$56$$

2. $$4$$

3. $$21$$

4. $$1$$
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