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

Share

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

View More Questions From Probability, Combinatorics

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 Arithmetic QuestionsPGDBA Progressions and Series QuestionsPGDBA Time Speed Distance QuestionsPGDBA Venn Diagrams QuestionsPGDBA Averages QuestionsPGDBA Percentages QuestionsPGDBA Time And Work QuestionsPGDBA Simple Interest Compound Interest QuestionsPGDBA Averages, Ratio and Proportion QuestionsPGDBA Linear Equations QuestionsPGDBA Probability, Combinatorics QuestionsPGDBA Number Systems QuestionsPGDBA Miscellaneous QuestionsPGDBA Coordinate Geometry QuestionsPGDBA Inequalities QuestionsPGDBA Averages Mixtures Alligations QuestionsPGDBA Mensuration QuestionsPGDBA Number Series QuestionsPGDBA Geometry QuestionsPGDBA Remainders QuestionsPGDBA Functions, Graphs and Statistics QuestionsPGDBA Algebra QuestionsPGDBA Profit and Loss QuestionsPGDBA Profit And Loss QuestionsPGDBA Time, Speed and Distance QuestionsPGDBA Logarithms QuestionsPGDBA Logarithms, Surds and Indices QuestionsPGDBA Data Sufficiency QuestionsPGDBA Quadratic Equations Questions

PGDBA DILR Questions | LRDI Questions For PGDBA

PGDBA Venn Diagrams QuestionsPGDBA 2D & 3D LR QuestionsPGDBA Games and Tournaments QuestionsPGDBA Special Charts QuestionsPGDBA Selection With Condition QuestionsPGDBA Arrangement QuestionsPGDBA Routes And Networks QuestionsPGDBA Data Interpretation QuestionsPGDBA Truth Lie Concept QuestionsPGDBA Puzzles QuestionsPGDBA Miscellaneous LR QuestionsPGDBA DI Miscellaneous QuestionsPGDBA Maxima-Minima QuestionsPGDBA Quant Based DI QuestionsPGDBA Data Interpretation Basics QuestionsPGDBA Data change over a period QuestionsPGDBA Charts QuestionsPGDBA Coins and Weights QuestionsPGDBA DI with connected data sets QuestionsPGDBA Scheduling QuestionsPGDBA Table based DI Sets QuestionsPGDBA Quant Based LR Questions

PGDBA Verbal Ability Questions | VARC Questions For PGDBA

PGDBA Grammar and Sentence Correction QuestionsPGDBA Odd One Out QuestionsPGDBA Vocabulary QuestionsPGDBA Critical Reasoning QuestionsPGDBA Para Summary QuestionsPGDBA Reading Comprehension QuestionsPGDBA Verbal Ability QuestionsPGDBA Para Jumbles Questions

Free PGDBA Quant Questions

PGDBA Data SufficiencyPGDBA LogarithmsPGDBA MiscellaneousPGDBA Averages, Ratio and ProportionPGDBA Venn DiagramsPGDBA Time, Speed and DistancePGDBA Probability, CombinatoricsPGDBA Averages Mixtures AlligationsPGDBA InequalitiesPGDBA Simple Interest Compound InterestPGDBA AveragesPGDBA Logarithms, Surds and IndicesPGDBA RemaindersPGDBA Functions, Graphs and StatisticsPGDBA Coordinate GeometryPGDBA Number SystemsPGDBA PercentagesPGDBA ArithmeticPGDBA Profit And LossPGDBA MensurationPGDBA Number SeriesPGDBA Time Speed DistancePGDBA AlgebraPGDBA Profit and LossPGDBA Linear EquationsPGDBA Quadratic EquationsPGDBA GeometryPGDBA Time And WorkPGDBA Progressions and Series

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored
CAT mentor

Join CAT 2026 course by 5-Time CAT 100%iler

Crack CAT 2026 & Other Exams with Cracku!

Enroll Now
Ask AI