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

Question

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

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] Choose the one integer among $1,\dots,98$ that maps to $1$: $98$ ways; all other integers $\le98$ map to $0$. The integers $99$ and $100$ may map to $0$ or $1$ freely: $2^2=4$ ways. Total $=98	imes4=392$. Answer: 392.

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

Explanation

Reviewed by Dr. Abubacker

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