Answer
$P(winning~Little~Lotto)=\frac{1}{575,757}\approx0.000001737$
Work Step by Step
The sample space: all the combinations of 39 distinct mumbers (from 1 to 39) taken 5 at a time:
$_{39}C_5=\frac{39!}{5!(39-5)!}=\frac{39!}{5!\times34!}$
But, $39!=39\times38\times37\times36\times35\times(34\times33\times32\times...\times3\times2\times1)=39\times38\times37\times36\times35\times34!$
$_{39}C_5=\frac{39\times38\times37\times36\times35\times34!}{5!\times34!}=\frac{39\times38\times37\times36\times35}{5\times4\times3\times2\times1}=\frac{69090840}{120}=575,757$
With one ticket: $N(winning~Little~Lotto)=1$
Using the Classical Method (page 259):
$P(winning~Little~Lotto)=\frac{N(winning~Little~Lotto)}{N(S)}=\frac{1}{575,757}\approx0.000001737$
