The product of any $r$ consecutive natural numbers is always divisible by

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$,then the number of ways in which they can be seated is

Let $A = \{a_1, a_2, a_3, ..., a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is:

$A$ parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed is

$A$ committee of $11$ members is to be formed from $8$ men and $5$ women. If $m$ is the number of ways to form the committee with at least $6$ men and $n$ is the number of ways to form the committee with at least $3$ women,then:

If $^nC_{12} = ^nC_6$,then $^nC_2 = $