Q: What is the probability of throwing 6 6sided die and getting a different number on each one?

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With 2 6-sided dices there are 6x6=36 combinations (6 for the first dice, 6 for the second dice) Let put the question this other way: how many combinations with a total more than 8, namely 9, 10, 11 or 12 ? 9: 4 combinations: 4-5 or 5-4 or 6-3 or 3-6 10: 3 combination: 5-5 or 6-4 or 4-6 11: 2 combinations: 6-5 or 5-6 12: 1 combination: 6-6 So there are 10 combinations for "more than 9" thus there are 36-10=26 combinations for "less or equal to 8".

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With 2 6-sided dices there are 6x6=36 combinations (6 for the first dice, 6 for the second dice) Let put the question this other way: how many combinations with a total more than 8, namely 9, 10, 11 or 12 ? 9: 4 combinations: 4-5 or 5-4 or 6-3 or 3-6 10: 3 combination: 5-5 or 6-4 or 4-6 11: 2 combinations: 6-5 or 5-6 12: 1 combination: 6-6 So there are 10 combinations for "more than 9" thus there are 36-10=26 combinations for "less or equal to 8".