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If n-1C3+n-...

Question

If $^{n - 1} C_{3} +^{n - 1} C_{4} >^{n} C_{3}$ , then n is just greater than integer

5

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Solution

The correct option is D $7$
$^{n - 1} C_{3} +^{n - 1} C_{4} >^{n} C_{3}$
$\Rightarrow^{n} C_{4} >^{n} C_{3} [∵^{n} C_{r} +^{n} C_{r + 1} =^{n + 1} C_{r + 1}]$
$\Rightarrow \frac{n!}{4! (n - 4)!} > \frac{n!}{3! (n - 3)!}$
$\Rightarrow \frac{1}{4} > \frac{1}{(n - 3)}$
$\Rightarrow n - 3 > 4 \Rightarrow n > 7$

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