If ^ⁿC_ 15 = ^ⁿC_6 then the value of ^ⁿC_ 21 is: - Vidyadip

MCQ

If $^\text{ⁿ}\text{C}_{15} = \ ^\text{ⁿ}\text{C}_6$ then the value of $\ ^\text{ⁿ}\text{C}_{21}$ is:

A
$0$
✓
$1$
C
$21$
D
None of these

✓

Answer

Correct option: B.

$1$

We know that
if $\ ^\text{ⁿ}\text{Cr}_1 =\ ^ⁿ\text{Cr}_2$
$\Rightarrow\text{n}= \text{r}^1 + \text{r}^2$
Given, $^\text{ⁿ}\text{C}_{15} = \ ^\text{ⁿ}\text{C}_6 $
$\Rightarrow\text{n} = 15 + 6$
$\Rightarrow\text{n} = 21$
Now, $ ^{21}\text{C}_{21} = 1$

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