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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2022 · Mathematics · Permutation and Combination

If C(3 n, 2 n)=C(3 n, 2 n-7) , then what is the value of C(n, n-5) ?

If C(3n,2n)=C(3n,2n−7)C(3 n, 2 n)=C(3 n, 2 n-7), then what is the value of C(n,n−5)C(n, n-5) ?

Options

  1. A42
  2. B35
  3. C28
  4. D21

Correct answer

D. 21

Step-by-step solution

Given that (3n2n)=(3n2n−7)\binom{3 n}{2 n}=\binom{3 n}{2 n-7}⇒2An+2n−7=3n⇒n=7∴nCn−5=7C2=7.62.1=21\begin{aligned} & \Rightarrow \quad 2 A n+2 n-7=3 n \\ & \Rightarrow \quad n=7 \\ & \therefore \quad{ }^n C_{n-5}={ }^7 C_2=\frac{7.6}{2.1}=21\end{aligned}$$
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