Andrew owns a commercial office building that is insured under $3$ property insurance contracts. He has $$100,000$ of insurance from Company A$,$ $$200,000$ from Company B and $$200,000$ from Company C$.$

$($a$)$ Assume that the pro rata liability provision appears in each contract. If a $$100,000$ loss occurs, how much will Andrew collect from each insurer? If a $$400,000$ loss occurs, how much will Andrew collect from each insurer? Explain your answer.

$($b$)$ Assume that the contribution of equal shares appears in each contract. If a $$100,000$ loss occurs, how much will Andrew collect from each insurer? If a $$400,000$ loss occurs, how much will Andrew collect from each insurer? Explain your answer.