Consider the following statements:

I. The number of positive integral solutions of $x_1+x_2+x_3+x_4=10$ is 286 .

II. If $25!=10^n \times k,(k \in \mathbf{N})$, then $n=6$

Which one of the following options is true?

A student is allowed to select at least $(n+1)$ books but not all books from a collection of ( $2 n+1$ ) books. If the total number of ways in which he can select these books is 255 , then the number of books in that collection is

Let $S_r=\{x, y, z) / x+y+z=11, x \geq r, y \geq r$, $z \geq r, x, y, z, r$ are integers $\}$ and $n\left(S_r\right)$ represents the number of elements in $S_r$. Then $n\left(S_{2)}+n\left(S_3\right)+n\left(S_4\right)=\right.$

A certain question paper contains three parts $A, B, C$ with four questions in part $A$, five questions in part $B$ and six questions in part $C$. A student is required to answer seven questions choosing at least two questions from each part. Then the total number of different ways a student can choose his seven questions for answering, is