Let $S=\{1,2,3,4,5,6\}$. Then the probability that a randomly chosen onto function $g$ from $S$ to $S$ satisfies $\mathrm{g}(3)=2 \mathrm{~g}(1)$ is :

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Permutations and Combinations

Let

S = {1, 2, 3, 4, 5, 6}

. Then the probability that a randomly chosen onto function

g

from

S

S

satisfies

g (3) = 2 g (1)

is :

Answer: (C)

An onto map from a finite set to itself is a bijection, so there are

6! = 720

of them. The condition

g (3) = 2 g (1)

forces

g (1) \in {1, 2, 3}

with

g (3) \in {2, 4, 6}

correspondingly, three admissible value-pairs, each leaving the other four elements to be permuted in

4!

ways. The favourable count is

3 \cdot 4! = 72

, so the probability is

\frac{72}{720} = \frac{1}{10}

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Single correct option