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# If $A=\{1,2,3,4\}\:and\:B=\{3,4,7\}$ then the no. of onto functions from $A\rightarrow B$=?

(A) 9 (B) 18 (C) 36 (D) 64
Can you answer this question?

Toolbox:
• If $n(A)=m\:and\:n(B)=n$ then, no. of onto functions from $A\rightarrow B$ is given by the formula : \begin {align} \sum \limits _{r=1} ^ {n}\end {align} $(-1)^{n-r}$ $^ n C_r$ $r^m$
By taking m=4 and n= 3 we get in the above formula
$(-1)^2$ $^3C_1$ $1^4$ $+(-1)^1$ $^3C_2$ $2^4$ $+(-1)^0$ $^3C_3$ $3^4$
$3-48+81=36$
answered May 27, 2013