Re: Making change probability question
You don't need brute force. If you have exactly a dollar, then of course you have change for a dollar. If you have more than a dollar then you have change for a dollar except for one case, three quarters and three dimes.
Therefore, figure out the expected number of coins you draw before getting $1.00 or more; and subtract off the correction for three quarters/three dimes.
This works for the other variants as well.
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