Question:
Let $S=\{1,2,3,4,5,6\} .$ Then the probability that a randomly chosen onto function g from $S$ to $S$ satisfies $g(3)=2 g(1)$ is :
Correct Option: 1
Solution:
$\mathrm{g}(3)=2 \mathrm{~g}(1)$ can be defined in 3 ways
number of onto functions in this condition $=3 \times 4 !$
Total number of onto functions $=6 !$
Required probability $=\frac{3 \times 4 !}{6 !}=\frac{1}{10}$