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6.Permutation and Combination
normal
$\left( {\begin{array}{*{20}{c}}n\\r\end{array}} \right) \div \left( {\begin{array}{*{20}{c}}n\\{n - 1}\end{array}} \right) = .........$
A
$\frac{{n - r}}{r}$
B
$\frac{{n + r - 1}}{r}$
C
$\frac{{n - r + 1}}{r}$
D
$\frac{{n - r - 1}}{r}$
Solution
$\left( {\begin{array}{*{20}{c}}
n \\
r
\end{array}} \right) \div \left( {\begin{array}{*{20}{c}}
n \\
{n – 1}
\end{array}} \right)$
$ = \frac{{n\,!}}{{r\,!\,(n – r)\,!}} \div \,\frac{{n\,!}}{{(r – 1)!\,(n – r + 1)\,!}}\,\,$
$\, = \frac{{n\,!}}{{r(r – 1)\,!\,(n – r)\,!}}.\,\frac{{(r – 1)!\,(n – r + 1)(n – r)\,!}}{{n\,!}}$
$ = \frac{{n – r + 1}}{r}$
Standard 11
Mathematics
