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What is the value of \(\frac{12!}{10!,2!}+\frac{8!}{6!,2!}\)?

Answer and explanation

Correct answer: 94

Here, the comma in each denominator indicates multiplication. Thus, \(\frac{12!}{10!\,2!}=\frac{12\times11}{2}=66\) and \(\frac{8!}{6!\,2!}=\frac{8\times7}{2}=28\). Therefore, the sum is \(66+28=94\). Option 90 can result from an error in multiplication or addition. Exam tip: Cancel common factorial terms first to simplify quickly.

Related tags

Factorial NotationBinomial CoefficientsPermutations And CombinationsClass 11 MathematicsFactorial SimplificationMathematicsClass 11 Mcq

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