MCQ
If ${^\text{20}}\text{C}_{\text{r}}={^\text{20}}\text{C}_{\text{r-10}}$ is then ${^\text{18}}\text{C}_{\text{r}}$ equal to:
  • A
    4896
  • B
    816
  • C
    1632
  • D
    None of these.

Answer

  1. 816

Solution:

$\text{r}+\text{r}-10=20$

$\Rightarrow 2\text{r}-10=20$

$\Rightarrow 2\text{r}=30$

$\Rightarrow \text{r}=15$

Now,

${^\text{18}}\text{C}_{\text{r}}={^\text{18}}\text{C}_{\text{15}}$

$\therefore\ {^\text{18}}\text{C}_{\text{15}}={^\text{18}}\text{C}_{\text{3}}$

$\therefore\ {^\text{18}}\text{C}_{\text{3}}=\frac{18}{3}\times\frac{17}{2}\times16$

$=816$

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