First slide

Combinations

Question

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

Moderate

A

n > 6
B

n > 7
C

n < 6
D

none of these

Solution

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

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