Problems from Factorial and combinatorial numbers

a) Calculate the following factorial: $$6!$$

b) Calculate the following combinatorial number: $$\displaystyle \binom{7}{2}$$

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Development:

a) $$6!=6\cdot5\cdot4\cdot3\cdot2\cdot1=720$$

b) $$$\displaystyle \binom{7}{2}=\frac{7!}{2!\cdot(7-2)!}=\dfrac{7!}{2!\cdot5!}=\dfrac{7\cdot6\cdot\not{5}\cdot\not{4}\cdot\not{3}\cdot\not{2}\cdot1}{2\cdot1\cdot\not{5}\cdot\not{4}\cdot\not{3}\cdot\not{2}\cdot1}=\dfrac{7\cdot6}{2}=21$$$

Solution:

a) $$6!=720$$

b) $$\displaystyle \binom{7}{2}=21$$

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