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Numbers that are divisible by 80 are itself and any of its other multiples

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Q: What numbers are dividable by 80?
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If one three-digit number is chosen at random from all those that can be made from the above set of digits find the probability that one is not multiple of 5?

An interesting question. The answer is 80%. A number must end in 0 or 5 to be dividable by 5. From 100 to 109 (10 numbers in total), there will be 2 numbers that are dividable by 5. If I then consider the entire set from 100 to 999 is 900 numbers, you have 90 sets of 10 numbers, each set with 2 dividable number, or 180/900 = 2/10 =20%. If 20% are dividable, 80% aren't. Suppose I extended the question, and say my set is all whole positive numbers and zero with n digits or less, where I pick n randomly from 1 to a million. If from this set, a number is picked randomly, what is the chance that it is dividable by 5. Answer: 20%.


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