Fifteen telephones have just been received at an authorized service center. Five are cellular, five are cordless, and five a conventional corded phones. If phones are randomly selected for service what is the probability that all the cordless phones are serviced first? What is the probability that after servicing ten phones, only two of the three types remain to be serviced?

My Work

Cellular - 5

Cordless - 5

Corded - 5

Sorry I don't know how to put the problem in Math symbol.

a) What is the probability that all the cordless phone are service first?

(5C5)(10C1)/(15C3) = (1)(10)/455 = .02 or 2%

b) What is the probability that after servicing ten telephones, only two of the three type remain to be service?

All I can come up is (10C2)(___)/(15C3)