Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
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) = $$2^{50}\left(2^{50}-1\right)$$
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
