Hello guys, I have a question and can't get a solid number. I want to know how many unique bitly links there are here is an example:

https://bit.ly/3nYKvHy (It doesn't lead anywhere it's just an example I promise)

In this problem the https://bit.ly/ remains constant, but how many combinations of 10 numbers, 26 uppercase letters,, and 26 lowercase letters are there in a 7 digit string?

Thanks in advance :)

Mr.Owl Jan 19, 2021

edited by
Guest
Jan 19, 2021

#1**+2 **

the number of unique characters = 10 + 26 + 26 = 62

the number of unique strings of 7 such characters = 62^{7} = 3 521 614 606 208

That's over 3 trillion!

hectictar Jan 19, 2021

#2**+1 **

Wow, that's a lot! Looks like bitly.com is going to stay in business for quite a while! Thanks for showing me how that works, I thought it might be calculated with permutations or something like 10+26+26=62

Then you need to calculate 62!, but that is just insanely big. And wrong lol. Thanks again!

Mr.Owl
Jan 19, 2021

#3**+2 **

Imagine there are only 4 characters: a, b, c, and d

And we want to know how many strings of length 3 can be made with those 4 characters.

First let's list all of the strings that start with 'a' :

aaa

aab

aac

aad

aba

abb

abc

abd

aca

acb

acc

acd

ada

adb

adc

add

There are 4 groups of 4 which means there are 4 * 4 = 16 strings in the above list.

Now imagine if we kept the pattern going. We could copy and paste the above list and change all of the first characters in each string to "b". Then we could paste it again and change all of the first letters to "c", and again for "d". That would make 4 total groups: the first group all start with "a", second group all start with "b", the third all start with "c" and the fourth all start with "d".

So then there would be a total of 4 * 4 * 4 = 4^{3} = 64 strings in the completed list.

So the total number of strings is 4^{3} , which is the number of different characters raised to the power of the length of the string.

I hope this helps explain a little bit where the 62^{7} comes from!

hectictar
Jan 20, 2021