Megamillions: odds of winning

Currently, the prize for Megamillions is over a billion dollars. Pick 5 numbers from 1 to 70, then pick one number from 1 to 25.

Odds of winning Megamillions:

25 Binomial[70, 5] = 302575350  

Not sure what the odds are of just one winner or no winners.

You can generate numbers with the following.

Append[RandomSample[Range[70], 5], RandomInteger[{1, 25}]]  

 {67, 51, 34, 25, 9, 10}
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