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Combination

If n-1C7+n-...

Question

If $^{n - 1} C_{7} +^{n - 1} C_{6} >^{n} C_{6}$ then

n > 4

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n > 12

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n \geq 13

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n > 13

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Solution

The correct option is D $n > 13$
Now,
$^{n - 1} C_{7} +^{n - 1} C_{6} >^{n} C_{6}$
or, $^{n - 1} C_{7} +^{n - 1} C_{7 - 1} >^{n} C_{6}$
or, $^{n} C_{7} >^{n} C_{6}$
or, $\frac{n!}{7! (n - 7)!} > \frac{n!}{6! (n - 6)!}$
or, $n - 6 > 7$
or, $n > 13$ .

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