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NDA 2020 Maths · Mathematics · Permutations and Combinations · easy

If binomn8=binomn12, then binomn2 equals

Single correct option

If (n8)=(n12)\binom{n}{8}=\binom{n}{12}, then (n2)\binom{n}{2} equals
  1. A. 190
  2. B. 210
  3. C. 120
  4. D. 171
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Answer: (A) 190

(nr)=(ns)\binom nr=\binom ns with r≠sr\ne s gives r+s=nr+s=n, so n=20n=20. Then (202)=20⋅192=190\binom{20}{2}=\dfrac{20\cdot19}{2}=190. The relation r=sr=s would give nothing here, and 210 is (212)\binom{21}{2}.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake