The total number of $4$-digit numbers whose greatest common divisor with $18$ is $3$ is .... .

The coefficient of $x^3 y^4 z^5$ in the expansion of $(x y+y z+x z)^6$ is

Consider the following statements:
$I$: The number of non-trivial even divisors of the number $N = 2^{\alpha_1} 3^{\alpha_2} 4^{\alpha_3} 5^{\alpha_4} 6^{\alpha_5}$ is $(\alpha_1+2\alpha_3+\alpha_5)(\alpha_2+\alpha_5+1)(\alpha_4+1)-1$.
$II$: The number of non-trivial odd divisors of the number $N = 2^{\alpha_1} 3^{\alpha_2} 4^{\alpha_3} 5^{\alpha_4} 6^{\alpha_5}$ is $\alpha_2+\alpha_4+\alpha_5+\alpha_2\alpha_4+\alpha_4\alpha_5$. Then:

What is the highest power of $3$ in $100!$?

The number of divisors of $7!$ is

The coefficient of $x^5$ in $(3+x+x^2)^6$ is