The number of integers between $1$ and $10^{10}$ (inclusive) that contain the digit $1$ is:

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

$\binom{n}{n-r} + \binom{n}{r+1}$,whenever $0 \le r \le n-1$,is equal to

Ten persons,among whom are $A, B$,and $C$,are to speak at a function. The number of ways in which they can speak if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is:

In an examination hall,there are $4$ rows of chairs. Each row has $8$ chairs,$1$ behind the other. There are $2$ classes sitting for the examination with $16$ students in each class. It is desired that in each row,all students belong to the same class and that no $2$ adjacent rows are allotted to the same class. In how many ways can these $32$ students be seated?

If $110$ triangles can be formed by joining $10$ points as vertices,in which $n$ points are collinear,then the value of $n$ is: