If all the six-digit numbers $x_1 x_2 x_3 x_4 x_5 x_6$ with $0 < x_1 < x_2 < x_3 < x_4 < x_5 < x_6$ are arranged in increasing order,then the sum of the digits in the $72^{\text{th}}$ number is $............$.

How many chords can be drawn through $21$ points on a circle?

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

If $x$ is the number of ways in which six women and six men can be arranged to sit in a row such that no two women are together and if $y$ is the number of ways they are seated around a table in the same manner,then $x: y=$ (in $: 1$)

How many parallelograms can be formed by a set of $4$ parallel lines intersecting another set of $3$ parallel lines?

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle formed by these three vertices is equilateral is