The sum is Odd
Probability
Level
2
Let S={1,2,...50} . Find out the number of ways one can choose a subset of S such that the summation of it's elements is odd.
2^30
2^48
2^49
2^25
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1 solution
It's very easy. The sum of the elements of S is 25x51,odd. Now whenever you choose a subset (A) with the sum of it's elements is odd ,then the sum of the elements of the remaining set or complimentary of A is even. Hence, the number of ways N odd = N even .And N odd+ N even= 2^50. So,N_odd= 2^49.