If ^ n + 1 C_3 = 2 ,^n C_2 , then n = - Vidyadip

MCQ

If $^{n + 1}{C_3} = 2{\,^n}{C_2},$ then $n =$

A
$3$
B
$4$
✓
$5$
D
$6$

✓

Answer

Correct option: C.

$5$

c
(c) $^{n + 1}{C_3} = 2\,.{\,^n}{C_2}$

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

==> $\frac{{n + 1}}{{3\,.\,2!}} = \frac{2}{{2!}}$

==> $n + 1 = 6\,\, \Rightarrow \,n = 5$.

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