$^n{C_r}\,{ \div ^n}{C_{r - 1}} = $
$\frac{{n - r}}{r}$
$\frac{{n + r - 1}}{r}$
$\frac{{n - r + 1}}{r}$
$\frac{{n - r - 1}}{r}$
(c) On simplifying you will get $\frac{{n – r + 1}}{r}$.
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 $……..$
Total number of $6-$digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is
A car will hold $2$ in the front seat and $1$ in the rear seat. If among $6$ persons $2$ can drive, then the number of ways in which the car can be filled is
If $^{n} C _{9}=\,\,^{n} C _{8},$ find $^{n} C _{17}$
From a class of $25$ students, $10$ are to be chosen for an excursion party. There are $3$ students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
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