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  • Let set 'A' has 7 elements and set B has 5 elements. If one function is selected from all possible defined functions from A to B then the pr

Let set 'A' has 7 elements and set B has 5 elements. If one function is selected from all possible defined functions from A to B then the probability that it is onto is

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\\\text{Total number of function from A to B }=5^{7}$ \\ Total number of onto functions from $A$ to $B$ is \\\\ $\mathrm{n}(\mathrm{E})=\frac{7 !}{3 ! 4 !} \times 5 !+\frac{7 !}{3 ! 2 !} \times \frac{1}{2 ! 2 !} \times 5 !$ \\\\ $=\frac{7 ! \times 20}{6}$\\\\ $\therefore \mathrm{P}(\mathrm{E})=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{7 ! \times 2}{3 \times 5^{6}}$

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