How long until bit.ly runs out of unique numbers?

This is an exercise for code newbies. It actually doesn't require any programming, just a little bit of calculation:

1. Consider a service such as bit.ly that generate short Urls

2. Assume that the generated key is always 7 alphanumeric characters long (using both upper case and lower case letters)

3. Suppose people around the world are generating short Urls at a rate of 1000 short Urls every second.

Question: How long takes until bit.ly runs out of unique sequences for the short Urls?

Comments

[Kay Kleinvogel]

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.

$$62^{6}=56,800,235,584‬$$

So now that we have the number of possible URLs we just have to divide it by the frequency of the URLs being created.

$$\frac{56,800,235,584‬}{1000} = 56,800,235.584 seconds$$

So bit.ly would run out in about ‬56,800,235 seconds (about 658 days).

[Adrian]

why 62 ^ 6?

[Kay Kleinvogel]

Should have read the task better. It's 7 digits so it should have been 62^7