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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
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  • 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 by rvidyagovindarajan_1
 

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