6. permutation and combination — ગણિત ધોરણ 11 સાયન્સ — Question

$r\,!\, = \,\frac{{30240}}{{252}} = 120 = 5\,!$

$r\, = \,5$

$\left( {\begin{array}{*{20}{c}}
  n \\ 
  5 
\end{array}} \right) = \frac{{n\,!}}{{(n - 5)\,!\,5\,!}} = 252$

$n(n - 1)(n - 2)(n - 3)(n - 4) = 252 \times 120$

$n(n - 1)(n - 2)(n - 3)(n - 4)$

$ = 10.6.2.9.7.4\, = \,10.9.8.7.6\,\,$

$n = 10\,\,\,\therefore \,(n,\,r) = (10,\,5)$