$15$ persons are sitting around a circular table. The number of ways of selecting three persons at a time from them,such that the selected three do not sit together at one place is

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 $............$.

If a group of six students including two particular students $A$ and $B$ stand in a row, then the probability of getting an arrangement in which $A$ and $B$ are separated by exactly one student in between them is

Six '$X$'s have to be placed in the squares of the figure such that each row contains at least one '$X$'. In how many different ways can this be done?

$A$ parallelogram is cut by two sets of $m$ parallel lines,each set being parallel to one of its sides. How many parallelograms are formed in total?

If the number of rectangles formed on a chessboard is $1296$,then the total number of squares formed on the chessboard is: