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If ${ }^n C_8={ }^n C_2$. Find ${ }^n C_2$.
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We have
$\begin{aligned}{ }^n \mathrm{C}_r &={ }^n \mathrm{C}_{n-r} \\{ }^n \mathrm{C}_2 &={ }^n \mathrm{C}_{n-2} \\{ }^n \mathrm{C}_8 &={ }^n \mathrm{C}_{n-2} \Rightarrow n-2=8 \text { or } n=10 \\{ }^n \mathrm{C}_2 &={ }^{10} \mathrm{C}_2=\frac{10 \times 9}{1 \times 2}=45 \end{aligned}$
$\begin{aligned}{ }^n \mathrm{C}_r &={ }^n \mathrm{C}_{n-r} \\{ }^n \mathrm{C}_2 &={ }^n \mathrm{C}_{n-2} \\{ }^n \mathrm{C}_8 &={ }^n \mathrm{C}_{n-2} \Rightarrow n-2=8 \text { or } n=10 \\{ }^n \mathrm{C}_2 &={ }^{10} \mathrm{C}_2=\frac{10 \times 9}{1 \times 2}=45 \end{aligned}$
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