What is the equation for calculating AT LEAST x 6s on y rolls on a six sided dice?

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For example, If I rolled $6$ dice how likely is it that I get $1$ or more $6$s? I know how to do exact binomial distribution but I'm not sure how to do figure out this situation.

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HINT:

Try to figure out what is the complement event. (This is best only for the case for the question in the body of your post)

For the general case look at saulspatz comment under your question.