First slide

Combinations

Question

if $^{n} C_{3} +^{n} C_{4} >^{n + 1} C_{3}$ ,then

Easy

A

$n > 6$
B

$n > 7$
C

$n < 6$
D

none of these

Solution

$^{n} C_{3} +^{n} C_{4} >^{n + 1} C_{3}$
$\Rightarrow^{n + 1} C_{4} >^{n + 1} C_{3}$ $(∵^{n} C_{r} +^{n} C_{r + 1} =^{n + 1} C_{r + 1})$
or $\frac{^{n + 1} C_{4}}{^{n + 1} C_{3}} > 1$
or $\frac{n - 2}{4} > 1$
or $n > 6$

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