Hello!
This is an exercise about factorials. To solve it, we have to expand the expressions, look:
[tex]\frac{8!\cdot5!}{9!\cdot2!}[/tex]Let's rewrite 9! in the denominator:
[tex]\frac{\cancel{8!}\cdot5!}{9\cdot\cancel{8!}\cdot2!}=\frac{5!}{9\cdot2!}[/tex]Note that as we have 8! in the numerator and denominator, we can cancel it.
Now, let's expand the expression 5!:
[tex]\frac{5\cdot4\operatorname{\cdot}3\operatorname{\cdot}\cancel{2!}}{9\operatorname{\cdot}\cancel{2!}}=\frac{5\operatorname{\cdot}4\operatorname{\cdot}3}{9}=\frac{60}{9}=\frac{20}{3}[/tex]In the same way, we can cancel 2!.
Simplifying the fractions, we will obtain the result as 20/3.
