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The sum of the series $S =^{20} C_{0} -^{20} C_{1} +^{20} C_{2} -^{20} C_{3} + \dots +^{20} C_{10}$ is

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20C10

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Correct option is B

Using nCr=nCn−r, we can write 2S=20C0−20C1+20C2−20C3+…20C10+20C20−20C19+ 20C18−…+20C10⇒ S=0+12 20C10=12 20C10

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The sum of the series S=20C0−20C1+20C2−20C3+…+20C10 is

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The sum of the series $S =^{20} C_{0} -^{20} C_{1} +^{20} C_{2} -^{20} C_{3} + \dots +^{20} C_{10}$ is