Last shiny penny arriving after the fourth draw

A box contains $3$ shiny and $4$ dull pennies, drawn one at a time without replacement. Find the probability that the third shiny penny is not obtained within the first $4$ draws.

$\tfrac{31}{35}$. All $\binom73=35$ placements of the shiny pennies in the draw order are equally likely. The third shiny one is within four draws only if all three shiny pennies lie in positions $1$–$4$, which happens in $\binom43=4$ placements, leaving $31$.