Q51 / 160 · WBJEE 2010 · Mathematics

If ${ }^{\mathrm{n}-1} \mathrm{C}_3+{ }^{\mathrm{n}-1} \mathrm{C}_4>{ }^{\mathrm{n}} \mathrm{C}_3$, then $\mathrm{n}$ is just greater than integer

  • A
    5
  • B
    6
  • C
    4
  • Correct answer
    D
    7

Solution

$$ \begin{aligned} & \text { Hints: }:^{n-1} C_3+{ }^{n-1} C_4>{ }^n C_3 \\ & \qquad \Rightarrow^n C_4>^n C_3 \Rightarrow \frac{n !}{4 !(n-4) !}>\frac{n !}{3 !(n-3) !} \Rightarrow \frac{1}{4}>\frac{1}{(n-3)} \Rightarrow n-3>4 \Rightarrow n>7 \end{aligned} $$

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

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