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

$7\frac{{n!}}{{(n - 3)!}} = 20\frac{{(n + 1)!}}{{(n - 1)!}}\,\,\,\,$

$\,\,7.\frac{{n!}}{{(n - 3)!}} = 20\frac{{(n + 1)n!}}{{(n - 1)(n - 2)(n - 3)!}}\,\,\,\,$

$7 = \frac{{20(n + 1)}}{{(n - 1)(n - 2)}}$

$7{n^2} - 21n + 14 = 20n + 20\,\,\,$

$7{n^2} - 41n - 6 = 0\,\,$

$\,\,7{n^2} - 42n + n - 6 = 0$

$(7n + 1) (n - 6) = 0 $ અને  $n  \in  N $

$n = 6 $ મળે.