Let S={1,2,3,4,5,6}. Then the probability that
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 :

  1. $\frac{1}{10}$

  2. $\frac{1}{15}$

  3. $\frac{1}{5}$

  4. $\frac{1}{30}$


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 $=\frac{3 \times 4 !}{6 !}=\frac{1}{10}$

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