In the town of Niceville, a local lottery is held once a year for the residents. Lottery tickets cost 50 cents apiece. Each lottery ticket contains four numbers, from 1 to 20. The lottery machine will select six numbers from 1 to 20. A winning ticket, worth $100, will contain four of the six numbers chosen by the machine.

Question

In the town of Niceville, a local lottery is held once a year for the residents. Lottery tickets cost 50 cents apiece. Each lottery ticket contains four numbers, from 1 to 20. The lottery machine will select six numbers from 1 to 20. A winning ticket, worth $100, will contain four of the six numbers chosen by the machine.
 
a)How much money would a person need to spend to buy every possible combination of four numbers?
 
b)What is the probability, to the nearest ten-thousandth, that a person will select four correct numbers?
 
c)To the nearest ten-thousadnth, what is the probability that a ticket has NO correct numbers?

Can you please explain how you got the answer also? Thanks so much~