So first we have to calculate the number of possible URLs.
Each character can has 62 possible outcomes (26 + 26 +10).
And we have 7 alphanumeric characters.
Since the order of the characters is important (/abcde != /edcba) we have to apply the permutation 👨🎓.
But since we are replacing characters we have chosen before (e.g. /aaaa is possible) we have to use permutations with replacements.
So now that we have the number of possible URLs we just have to divide it by the frequency of the URLs being created.
So bit.ly would run out in about 56,800,235 seconds (about 658 days).
why 62 ^ 6?
Should have read the task better. It's 7 digits so it should have been 62^7
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