Q163 / 270 · NDA 2022 (Phase 1) · Mathematics

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

  • A
    42
  • B
    35
  • C
    28
  • Correct answer
    D
    21

Solution

Given that ${ }^{3 n} C_{2 n}={ }^{3 n} C_{2 n-7}$ $\begin{aligned} & \Rightarrow \quad 2 A n+2 n-7=3 n \\ & \Rightarrow \quad n=7 \\ & \therefore \quad{ }^n C_{n-5}={ }^7 C_2=\frac{7.6}{2.1}=21\end{aligned}$

Hence, the correct answer is option: 'D'.

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