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  3. Find the number of onto functions from A to B where n(A) = 5 and n(B) = 3
# Engineering

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

Answers (1)
A Akshay

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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