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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2019 · Mathematics · Permutation and Combination

If C(20, n+2)=C(20, n-2) , then what is n equal to?

If C(20,n+2)=C(20,n−2)\mathrm{C}(20, \mathrm{n}+2)=\mathrm{C}(20, \mathrm{n}-2), then what is n equal to?

Options

  1. A8
  2. B10
  3. C12
  4. D16

Correct answer

B. 10

Step-by-step solution

Given, C(20,n+2)=C(20,n−2)C(20, \mathrm{n}+2)=\mathrm{C}(20, \mathrm{n}-2)⇒20Cn+2=20Cn−2⇒20=n+2+n−2(∵ncr=ncs⇒n=r+s)⇒20=2n⇒n=10\begin{aligned} & \Rightarrow{ }^{20} \mathrm{C}_{\mathrm{n}+2}={ }^{20} \mathrm{C}_{\mathrm{n}-2} \\ & \Rightarrow 20=\mathrm{n}+2+\mathrm{n}-2 \quad\left(\because^n c_r={ }^n c_s \Rightarrow n=r+s\right) \\ & \Rightarrow 20=2 \mathrm{n} \\ & \Rightarrow \mathrm{n}=10\end{aligned}$$
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