a) Calculate the following factorial: $$6!$$
b) Calculate the following combinatorial number: $$\displaystyle \binom{7}{2}$$
See development and solution
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) $$\displaystyle \binom{7}{2}=21$$