B.10 At least one

Out of n items, take at least one item each time.

• □ □ □ \(\cdots\) □ Each item can or cannot be taken (having 2 options).
• \(\rightarrow 2^n - 1\) (1 \(\leftarrow\) no items included)

Alternative

• \({n \choose 1} + {n \choose 2} + {n \choose 3} + \cdots + {n \choose n}\)
• \(\{1 + ^nC_1 \cdot 1 + ^nC_2 \} \cdot 1^2+ \cdots 1^n \} -1\)
• \((1+1)^n-1\)
• \(2^n - 1\)