First slide

Combinations

Question

If $\frac{1}{^{4} C_{n}} = \frac{1}{^{5} C_{n}} + \frac{1}{^{6} C_{n}}$ , then value of $n$ is

Moderate

A

3
B

4
C

1
D

2

Solution

$\begin{array}{l} \frac{^{5} C_{n}}{^{4} C_{n}} = 1 + \frac{^{5} C_{n}}{^{6} C_{n}} \\ \Rightarrow \frac{5}{5 - n} = 1 + \frac{6 - n}{6} \\ \Rightarrow n^{2} - 17 n + 30 = 0 \Rightarrow n = 2 . \end{array}$

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