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Class 11MathematicsPermutations and CombinationsCombinationsMedium
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In how many ways can at least (2) and at most (3) gifts be selected from (11) different gifts?

Answer and explanation

Correct answer: 220

The selection may contain either 2 gifts or 3 gifts. Therefore, the total number of ways is \(\binom{11}{2}+\binom{11}{3}=55+165=220\). Option 165 counts only the selections of 3 gifts and does not include selections of 2 gifts. Exam tip: Add the combinations for every permitted selection size between “at least” and “at most.”

Related tags

CombinationsPermutations And CombinationsClass 11Selection CountingBinomial CoefficientsMathematicsClass 11 Mcq
सुधार सुझाएँ / Earn

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  9. 9If \(\frac{(n+2)!}{(n-2)!}=3024\), what is the value of \(n\)?
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