Solution:
Total no. of subsets =
We have,
Sum of elements will be 203 if we would not choose 7 or elements which are giving sum 7.
Elements giving sum 7 are (1, 6), (2, 5), (3, 4), (1, 2, 4) Thus, a subset will be 'nice' if we didn't choose these 5 outcomes.
Required probability (subset choosen is 'nice')