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Combinations — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsCombinations1 Mark
MCQ
If ${^\text{20}}\text{C}_{3\text{r+1}}={^\text{20}}\text{C}_{\text{r-1},}$ is then $r$ equal to : 
  • ✓
    $10$
  • B
    $11$
  • C
    $19$
  • D
    $12$
✓

Answer

Correct option: A.
$10$
$\text{r}+\text{1}+\text{r}-1=20$
$[\therefore \ ^\text{n}\text{C}_{\text{x}} = \ ^\text{n}\text{C}_{\text{y}} \Rightarrow \text{n} = \text{x} + \text{y} \text{ or } \text{x = y}]$
$\Rightarrow 2\text{r}=20$
$\Rightarrow \text{r}=10$

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