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Class 11MathematicsPermutations and CombinationsCombinationsEasy
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In how many ways can at least (2) colors be selected from (6) colors?

Answer and explanation

Correct answer: 57

Each of the 6 colours has two possibilities: selected or not selected. Hence, there are \(2^6=64\) total subsets. The 1 selection with no colour chosen and the \(\binom{6}{1}=6\) selections with exactly one colour chosen are not allowed. Therefore, the required number is \(64-1-6=57\). Option 63 excludes only the empty selection, but selections of exactly one colour must also be excluded. Exam tip: For “at least” questions, counting the complement is often quicker.

Related tags

CombinationsPermutations And CombinationsClass 11Subset CountingComplement CountingMathematicsClass 11 Mcq
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