If ^n+1C_3 = 2 ^ⁿC_2, then the value of n is: - Vidyadip

MCQ

If$\ ^\text{n+1}\text{C}_3 = 2\ ^\text{ⁿ}\text{C}_2,$ then the value of $n$ is:

A
$3$
B
$4$
C
$5$
✓
$6$

✓

Answer

Correct option: D.

$6$

Given,$\ ^\text{n+1}\text{C}_3 = 2\ ^\text{ⁿ}\text{C}_2,$
$\Rightarrow\bigg[\frac{(\text{n + 1})!}{(\text{n} + 1 – 3)}\times3!\bigg] = \frac{2\text{n}!}{(\text{n} – 2)}\times2!$
$\Rightarrow\bigg[\frac{(\text{n}\times1!)}{(\text{n}-2)}\times3!\bigg] = \frac{2\text{n}!}{(\text{n} – 2)}\times2$
$\Rightarrow\frac{\text{n}}{3!} = 1$
$\Rightarrow\frac{\text{n}}{6} = 1$
$\Rightarrow\text{n} = 6$

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