JEE Main 2021 (Online) 31st August Evening ShiftQuestion 1
Let $S=\{1,2,3,4,5,6\}$. Then the probability that a randomly chosen onto function $g$ from $S$ to $S$ satisfies $g(3)=2g(1)$ is :
Probability
Solution
Onto $S\to S$ means bijection: $6!=720$. $g(3)=2g(1)$: $(g(1),g(3))=(1,2),(2,4),(3,6)$. Remaining 4 elements map bijectively to remaining 4 values: $4!=24$ each. Favourable $=72$; $P=\frac{72}{720}=\frac1{10}$. Option C.