If ^ 18 C_x= ^ 18 C_ x+2 , Find x. - Vidyadip

Question

If ${ }^{18} C_x={ }^{18} C_{x+2}$, Find $x$.

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Answer

We have, If ${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{p}}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{q}}=\mathrm{n}$ Then $\mathrm{p}+\mathrm{q}=\mathrm{n}$ Also, ${ }^{18} \mathrm{C}_{\mathrm{x}}={ }^{18} \mathrm{C}_{\mathrm{x}+2}$ $\Rightarrow \mathrm{x}+\mathrm{x}+2=182 \mathrm{x}+2=182 \mathrm{x}=18-22 \mathrm{x}=16 \mathrm{x}=8$

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