Probability that numbers 1…6 show up at least once when rolling 10 dice

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Probability that numbers 1…6 show up at least once when rolling 10 dice. I know that it is a duplicate question here. The problem is I do not understand the answer. Can someone explain it more intuitively? Specially case 2 and 3 from the link. I understand, btw the inclusion-exclusion principle in set theory, but not here among probabilities. I know I am asking a simple question. Sorry for that!