If ${ }^n C_7={ }^n C_6$, then ${ }^n C_2=$

If ${ }^n C_7={ }^n C_6$, then ${ }^n C_2=$
  1. 858
  2. 13
  3. 1
  4. 78

Solution

$ \begin{aligned} & \text { Given, }{ }^n C_7={ }^n C_6 \\ & \begin{array}{l} \Rightarrow n=7+6=13\left\{\text { If }{ }^n C_x={ }^n C_y \Rightarrow \text { either } x=y\right. \text { or } \\ x+y=n\} \end{array} \\ & \therefore{ }^n C_2={ }^{13} C_2=\frac{13 \times 12}{2}=13 \times 6=78 \end{aligned} $ Hence, option (4) is correct

Asked in: AP EAMCET 2020 (22 Sep Shift 1)

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