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A super-mega-jackpot game that draws 6 numbers from 1 - 70 from a single machine and then a Super-Mega-Match ball numbered 1 - 30 from

A super-mega-jackpot game that draws 6 numbers from 1 - 70 from a single machine and then a Super-Mega-Match ball numbered 1 - 30 from a separate machine.

What is the probability of winning the Super-Mega jackpot by matching all six numbers and the Super-Mega-Match ball?
What is the probability of winning the jackpot by matching all six numbers, but not matching the Super-Mega-Match ball?
What is the probability of not matching any numbers on a ticket?

Please show all work with each solution.

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