A game of Lotto 6/42 is played where out of the numbers 1 through 42, six are selected without regard to order, and a jackpot draw is to choose your 6 numbers to be the same as the drawn ones. A billionaire finds that the jackpot is 27.5 million dollars, so she buys 15 million tickets and has the lotto computer pick the draws randomly; the other citizens buy 10 million tickets and fill them in by the same method. What is the probability that the billionaire will be among the winners of the jackpot? What is the probability that the billionaire will be the only winner of the jackpot?

Please solve