Let S = {1, 2, ..., 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is "nice" is:

total no. of ways subset of S can be formed =220no. of ways in which word nice comes if sum of the elements =203sum of all elements of S =21×202=210so sets can be1,2,.5,6,8.20 in this sum7is ommited and this formation ofsum can be done in5ways(7,(1,6),(2,5),(3,4),(1,2,4))waysprobability=5220