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Permutation and Combinations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPermutation and Combinations1 Mark
MCQ
If $^nC_{12}=^nC_8 ,$ then n is equal to.
  • ✓
    $20$
  • B
    $12$
  • C
    $6$
  • D
    $30$
✓

Answer

Correct option: A.
$20$
Give that $^\text{n}\text{C}_{12}=\ ^\text{n}\text{C}_8[\because\ ^\text{n}\text{C}_\text{r}=\ ^\text{n}\text{C}_\text{n-r}]$
$^\text{n}\text{C}_{12}=\ ^\text{n}\text{C}_\text{n-8}$
$\therefore\text{n}-8=12$
$\Rightarrow\text{n}=12+8$
$=20$

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