S={1,…,20}. A subset B is "nice" if the sum of its elements is 7 *(note: the source solution actually finds sets summing to 7, though the stem states 203 --- likely an OCR digit-swap of "7")*. Find the probability a random subset is "nice".
Solutions · 1
Official solution
Total subsets =220. Subsets summing to 7: {7},{1,6},{2,5},{3,4},{1,2,4} --- 5 subsets.
\[P = \frac{5}{2^{20}}\]