Mathematics - Functions Question with Solution | TestHub

If set $A$ has $m$ elements and set $B$ has $\mathrm{n}$ elements then number of onto functions from $A$ to $B$ is ${\sum }_{r=1}^n(-1{)}^{n-r}{}^n{C}_r{r}^m\text{ where }1\le n\le m$ Here $E=\{1,2,3,4\},F=\{1,2\}$ $m=4,n=2$ $\therefore$ No. of onto functions from $\mathrm{E}$ to $\mathrm{F}$ $\begin{array}{rl}& =\sum _{r=1}^2(-1{)}^{2-r2}{C}_r(r{)}^4\\ & =(-1{)}^2{C}_1+{}^2{C}_2(2{)}^4=-2+16=14\end{array}$