Factorial and combinatorial numbers
a) Calculate the following factorial: $6!$
b) Calculate the following combinatorial number: $\displaystyle \binom{7}{2}$
a) $6!=6\cdot5\cdot4\cdot3\cdot2\cdot1=720$
b) $$\displaystyle \binom{7}{2}=\frac{7!}{2!\cdot(7-2)!}=\dfrac{7!}{2!\cdot5!}=\dfrac{7\cdot6\cdot\not{5}\cdot\not{4}\cdot\not{3}\cdot\not{2}\cdot1}{2\cdot1\cdot\not{5}\cdot\not{4}\cdot\not{3}\cdot\not{2}\cdot1}=\dfrac{7\cdot6}{2}=21$$
a) $6!=720$
b) $\displaystyle \binom{7}{2}=21$