S=1,,6.

Question

$S=\{1,\dots,6\}$. Find the probability that a randomly chosen onto function $g:S	o S$ satisfies $g(3)=2g(1)$.

Accepted Answer

Total onto (bijective) functions $=6!$. Valid $(g(1),g(3))$ pairs: $(1,2),(2,4),(3,6)$ --- 3 cases, each with $4!$ arrangements for the rest.

$$P = \frac{3\times4!}{6!}=\frac{1}{10}$$

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