Question

Show that 9!/3!6! +9! /4!5! = 10! /4!6!​

Answer 1

I assume it's $\dfrac{9!}{3!6!}+\dfrac{9!}{4!5!}=\dfrac{10!}{4!6!}$

$\dfrac{9!}{3!6!}+\dfrac{9!}{4!5!}=\dfrac{10!}{4!6!}\\\\\dfrac{7\cdot8\cdot9}{2\cdot3}+\dfrac{6\cdot7\cdot8\cdot9}{2\cdot3\cdot4}=\dfrac{7\cdot8\cdot9\cdot10}{2\cdot3\cdot4}\\\\7\cdot4\cdot3+7\cdot2\cdot9=7\cdot3\cdot10\\7\cdot2\cdot 3\cdot(2+3)=7\cdot2\cdot3 \cdot 5\\2+3=5\\5=5$