$1.$ T$,$ a single taxpayer, has a salary of $$200,000$ in the current year. T also has the following transactions all involving the sale of capital assets: $(1)$ a gain of $$15,000$ on a $$collectible$$ held for $2$ years; and $(2)$ a gain of $$20,000$ on stock held for $15$ months.

$($a$)$Determine the amount of T$$s net capital gain.

$($b$)$At what rate will the components of T$$s net capital gain be taxed?

$($c$)$Assuming there is a flat $30\%$ tax on ordinary income and disregarding any deductions $($including the standard deduction and personal exemption$),$ what is T$$s tax liability in the current year?