Number of functions f:1,2, ,100 0,1, that assign 1 to exactly one of the positive integers…

Question

Number of functions $f:{1,2,\ldots ,100}	o {0,1}$, that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to \_\_\_\_\_\_\_\_.

Answer: 392

Accepted Answer

Exactly one of the first $98$ integers maps to $1$: choose which one, $98$ ways. The remaining $97$ of the first $98$ must map to $0$ (fixed). The last two elements ($99,100$) can independently map to $0$ or $1$: $2^2=4$ ways.

$$\text{Total} = 98 \times 4 = 392$$

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