ThermalPro is a distributor of temperature control equipment and has a June $30$ year$-$end. Dividends were last paid in $2018($dividends related to $2018$ and prior years were paid in $2018$ and no additional dividends were paid in $2019$ or $2020).$

On June $30,2021$ the company declared $$120,000$ of dividends. As at June $30,2021,$ the following shares were outstanding:

$$ $$0\mathrm{.}35$ Preferred shares, $75,000$ issued and outstanding...................$$375,000.$

$$ Common shares, $90,000$ issued and outstanding............................$$360,000.$

Calculate how much ThermalPro owes in dividends to each of the shareholders as at June $30,2021$ in each of the following three scenarios:

$($a$)$ Preferred shares are non$-$cumulative and non$-$participating.

$($b$)$ Preferred shares are cumulative and non$-$participating.

$($c$)$ Preferred shares are cumulative and participating.