Q65 / 160 · AP EAMCET 2011 · Mathematics

If ${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$, then the minimum value of $n$ is

  • A
    5
  • B
    6
  • C
    7
  • Correct answer
    D
    8

Solution

Given, ${ }^{n-1} C_3+{ }^{n-1} C_4>{ }^n C_3$ $\begin{array}{lc} \therefore & { }^n C_4>{ }^n C_3 \\ & {\left[\because{ }^n C_r+{ }^n C_{r-1}={ }^{n+1} C_r\right]} \\ \Rightarrow & n-4>3 \\ \Rightarrow & n>7 \\ \therefore & n=8 \end{array}$

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

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