Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1}-T_n=10$,then the value of $n$ is

In a tournament with five teams,each team plays against every other team exactly once. Each game is won by one of the playing teams and the winning team scores one point,while the losing team scores zero. Which of the following is $NOT$ necessarily true?

In a row,$6$ boys and $6$ girls are arranged at random. Find the probability that all $6$ girls are together.

If a polygon has $44$ diagonals,then it has ...... sides.

$A$ rectangle with side lengths $2m - 1$ and $2n - 1$ is divided into unit squares by drawing parallel lines as shown. How many rectangles are there such that both side lengths are odd?

$A$ tea party is arranged for $16$ people at a long table with $8$ chairs on each side. $4$ specific people wish to sit on one particular side and $2$ on the other side. In how many ways can they be seated?