Number of onto functions from A to B = n(A)Cn(B) = 5C3 = 10

As we have learned

Number of Onto function -

$f:A\rightarrow B$

$Such\: that\: n\left ( A \right )= m$

&                    $n\left ( B\right )=n$

$m\geqslant n$

Number of onto functions $= \sum_{r=1}^{n}\left ( -1 \right )^{n-r}n_{C_{r}}r^{m}$

-

$\sum_{r=1}^3{}(-1)^{3-r} C_{r}^{3}\textrm{} * {r^{5}}$

$\Rightarrow C_{1}^{3}\textrm{}- C_{2}^{3}\textrm{}* 2^5+ C_{3}^{3}\textrm{}*3^5$

$\Rightarrow 3-96+243\Rightarrow 243-93$

= 150

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