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Model Paper 5 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 51 Mark
MCQ
If $P(n, r) = C(n, r)$ then
  • A
    $r = 0$ or $2$
  • B
    $r = 1$ or $ n$
  • ✓
    $r = 0$ or $1$
  • D
    $n = r$
✓

Answer

Correct option: C.
$r = 0$ or $1$
Given $P ( n , r )= C ( n , r )$
$\Rightarrow \frac{n!}{(n-r)!}=\frac{n!}{r!(n-r)!}$
$\Rightarrow 1=\frac{1}{r!}$
$\Rightarrow r!=1$
$\Rightarrow r=0 \text { or } r=1[\because 0!=1,1!=1]$

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