Let
S={x1,x2,x3,x4,x5,x6,x7} Let the chosen element be
xi Total number of subsets of
S=27=128 No. of non-empty subsets of
S=128−1=127 We need to find number of those subsets that contains
xi.
x1x2−−−−−−−xi−−−−x7 For those subsets containing
xi , each element has 2 choices.
i.e., (included or not included) in subset,However as the subset must contain
xi,xi has only one choice. (included one)
So, total no. of subsets containing
xi=2×2×2×2×1 ×2×2=64 =