Q100 / 180 · COMEDK 2023 (Memory Based) · Mathematics

Find ${ }^n C_{21}$, if ${ }^n C_{10}={ }^n C_{12}$

  • A
    1
  • B
    21
  • Correct answer
    C
    22
  • D
    2

Solution

We know that if ${ }^n C_x={ }^n C_y$, then either $x=y$ or $x+y=n$ Since, ${ }^n C_{10}={ }^n C_{12}$ $\begin{aligned} \therefore \quad 10+12 & =n \\ \Rightarrow \quad n & =22 \\ \text { Now, }{ }^n C_{21} & ={ }^{22} C_{21} \\ & =\frac{22 !}{(22-21) ! 21 !}=\frac{22 !}{1 ! 21 !}=\frac{22 \times 21 !}{1 \times 21 !}=22 \end{aligned}$

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

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