Question 49
Let S = {1,2,...,100}. The number of nonempty subsets T of S such that the, product of numbers in T is even is
Solution
The number of ways to select non-empty set out of S = 100C1+100C2+100C3+..........100C100 = $$2^{100}$$-1
Similarly, the number of ways to select non-empty set from (say) P= {1,3,5,7,9,...................99} = $$2^{50}$$-1
Hence, the required number of set = $$2^{100}$$-1 - ($$2^{50}$$-1) = $$2^{50}\left(2^{50}-1\right)$$
Get AI Help
Create a FREE account and get:
- All Quant Formulas and shortcuts PDF
- 40+ previous papers with solutions PDF
- Top 500 MBA exam Solved Questions for Free
PGDBA Quant Questions | PGDBA Quantitative Ability
PGDBA Profit And Loss QuestionsPGDBA Number Systems QuestionsPGDBA Functions, Graphs and Statistics QuestionsPGDBA Logarithms, Surds and Indices QuestionsPGDBA Logarithms QuestionsPGDBA Profit and Loss QuestionsPGDBA Progressions and Series QuestionsPGDBA Remainders QuestionsPGDBA Simple Interest Compound Interest QuestionsPGDBA Probability, Combinatorics QuestionsPGDBA Miscellaneous QuestionsPGDBA Time, Speed and Distance QuestionsPGDBA Geometry QuestionsPGDBA Data Sufficiency QuestionsPGDBA Linear Equations QuestionsPGDBA Quadratic Equations QuestionsPGDBA Averages QuestionsPGDBA Mensuration QuestionsPGDBA Coordinate Geometry QuestionsPGDBA Number Series QuestionsPGDBA Percentages QuestionsPGDBA Averages Mixtures Alligations QuestionsPGDBA Time Speed Distance QuestionsPGDBA Time And Work QuestionsPGDBA Arithmetic QuestionsPGDBA Inequalities QuestionsPGDBA Averages, Ratio and Proportion QuestionsPGDBA Algebra QuestionsPGDBA Venn Diagrams Questions
PGDBA DILR Questions | LRDI Questions For PGDBA
PGDBA Venn Diagrams QuestionsPGDBA Data change over a period QuestionsPGDBA Truth Lie Concept QuestionsPGDBA Scheduling QuestionsPGDBA Charts QuestionsPGDBA Arrangement QuestionsPGDBA Special Charts QuestionsPGDBA Quant Based DI QuestionsPGDBA Puzzles QuestionsPGDBA 2D & 3D LR QuestionsPGDBA Data Interpretation QuestionsPGDBA Quant Based LR QuestionsPGDBA Table based DI Sets QuestionsPGDBA Coins and Weights QuestionsPGDBA Selection With Condition QuestionsPGDBA Data Interpretation Basics QuestionsPGDBA Games and Tournamnents QuestionsPGDBA DI Miscellaneous QuestionsPGDBA Routes And Networks QuestionsPGDBA DI with connected data sets QuestionsPGDBA Maxima-Minima QuestionsPGDBA Miscellaneous LR Questions
PGDBA Verbal Ability Questions | VARC Questions For PGDBA
Free PGDBA Quant Questions
PGDBA AveragesPGDBA Time Speed DistancePGDBA PercentagesPGDBA Time, Speed and DistancePGDBA MiscellaneousPGDBA Probability, CombinatoricsPGDBA Averages Mixtures AlligationsPGDBA Coordinate GeometryPGDBA Profit and LossPGDBA GeometryPGDBA Progressions and SeriesPGDBA ArithmeticPGDBA Quadratic EquationsPGDBA Profit And LossPGDBA Number SeriesPGDBA Functions, Graphs and StatisticsPGDBA MensurationPGDBA Logarithms, Surds and IndicesPGDBA LogarithmsPGDBA Number SystemsPGDBA Simple Interest Compound InterestPGDBA Averages, Ratio and ProportionPGDBA InequalitiesPGDBA RemaindersPGDBA Time And WorkPGDBA Data SufficiencyPGDBA Venn DiagramsPGDBA Linear EquationsPGDBA Algebra
