$^n{C_r}\,{ \div ^n}{C_{r - 1}} = $
$\frac{{n - r}}{r}$
$\frac{{n + r - 1}}{r}$
$\frac{{n - r + 1}}{r}$
$\frac{{n - r - 1}}{r}$
Let $S=\{1,2,3,5,7,10,11\}$. The number of nonempty subsets of $S$ that have the sum of all elements a multiple of $3$ , is $........$
A father with $8$ children takes them $3$ at a time to the Zoological gardens, as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is
In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation
If $^{n + 1}{C_3} = 2{\,^n}{C_2},$ then $n =$
Let $A = \left\{ {{a_1},\,{a_2},\,{a_3}.....} \right\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of it is formed independently. The number of ways in which subsets can be formed such that $(P-Q)$ contains exactly $2$ elements, is