A set S containing elements {1, 2, 3, 4, 5, 6, 7, 8}. The number of elements in S (n) is 8.

Since the set size is 8, simply calculate powers of 2: $2^1=2, 2^2=4, 2^3=8, 2^4=16, 2^5=32, 2^6=64, 2^7=128, 2^8=256$.

Students often mistakenly calculate $2 \times n$ (which is 16) instead of $2^n$ (which is 256).

This concept of subsets is fundamental to probability where the total number of outcomes in a sample space is often a power of 2 when dealing with binary events like coin tosses (e.g., $2^n$ outcomes for $n$ coins).