## 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

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