All possible two factors products are formed from numbers $1, 2, 3, 4, ...., 200$. The number of factors out of the total obtained which are multiples of $5$ is

$^{14}{C_4} + \sum\limits_{j = 1}^4 {^{18 - j}{C_3}} $ is equal to

The number of onto functions $f$ from $\{1, 2, 3, …, 20\}$ only $\{1, 2, 3, …, 20\}$ such that $f(k)$ is a multiple of $3$, whenever $k$ is a multiple of $4$, is

The number of matrices of order $3 \times 3$, whose entries are either $0$ or $1$ and the sum of all the entries is a prime number, is$....$

Words of length $10$ are formed using the letters, $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated ; and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, $\frac{y}{9 x}=$

If $\frac{{{}^{n + 2}{C_6}}}{{{}^{n - 2}{P_2}}} = 11$, then $n$ satisfies the equation