I found the n-word, all-caps, in a YouTube video id ... I'm just trying to find the probability of that happening, it made me incredibly curious.

What I know is: -there are 11 characters in a video id -there are 63 possible characters (A-Z, a-z, 0-9, -, _)

Can anyone help me with a specific problem I have with this? ;

I know that the probability is favorable outcomes/total outcomes. In the case of a 5-letter long video id, the favorable outcomes would be 1, and the total would be 63, and then you multiply them by themselves 5 times, so you get P = 1/63⁵ (which already sounds insane, huh??).

But I also know that if the length of the video id increases, there are more possible spaces where the n-word could appear in all caps. In the case of YouTube, they're 11 characters long. So there are 7 possible spaces where the n-word could appear. I don't know how to account for that increase, though. Do I just multiply 1/63⁵ by 7, getting 7/63⁵?