Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$. Then the number of many-one functions $f:A o B$ such that $1\in f(A)$ is equal to :

Question

Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$. Then the number of many-one functions $f:A	o B$ such that $1\in f(A)$ is equal to :

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] Functions with $1$ in the range: $4^4-3^4=175$. The one-one functions (bijections) all contain $1$ in the range: $4!=24$. Many-one $=175-24=151$. Answer (1).

Q. Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$. Then the number of many-one functions $f:A\to B$ such that $1\in f(A)$ is equal to :

Explanation

Reviewed by Dr. Abubacker

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