Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationnPr & nCrMedium2 minPYQ_2019

MathematicsMediumsingle choice

Let $S = \{1, 2, 3, \dots ., 100\}$ , then number of non-empty subsets $A$ of $S$ such that the product of elements in $A$ is even is :

Answer:

Solution:

As we know that the product of numbers is even when at least one of the number must be even.

Hence total subsets of $A$ in which product of numbers is even $=$ Total subsets $-$ total subsets in which all the elements are odd

$= 2^{100} - 2^{50} = 2^{50} (2^{50} - 1)$ .

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: PYQ_2019

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