What is the possible number of unique google meet codes? This is a sample google meet code: kgk-imsy-era
Any idea how many such unique codes can be there?
Given that a particular letter in the code may or may not repeat. If it repeats, we do not know how may times it'll repeat.
Is it something like
$$^{10}C_{x} \cdot 26^{x} \cdot ^{25}P_{(10-x)} + ^{26}P_{10}$$
where, x = number of times a particular letter is repeated

Few points to note:

*

*The codes are always composed of 10 letters (and no numbers)

*The codes are case-insensitive

*The hyphens in between are just used to separate the letters and are not a part of the code


Thanks!
 A: I do not know about the procedure of google meeting codes , but i will write my answer according to given information by you.
We have two option such that a particular letter repeat or not repeat.
If it the particular letter does not repeat :
Firstly ,select this letter by $C(26,1)=26$ ways and select the rest by $C(25,9)$.After that arrange them by $P(10,10)$ .Then the answer is $$C(26,1) \times C(25,9) \times P(10,10)$$
If it the particular letter does  repeat :
Firstly ,select this letter by $C(26,1)=26$ ways .However , we do not know how many times it will repeat ,so we will use generating function to calculate the all possible arrangements of letters such that
Generating function for selected letter = $$ \frac{x^2}{2} + \frac{x^3}{3!} + ..$$
$\color{red}{NOTE=}$ We started by $\frac{x^2}{2!}$ to avoid overcounting when the letter occurs only once
Generating function for the rest of  letters = $$1+ x + \frac{x^2}{2!} + \frac{x^3}{3!} + ..$$
So ,we should find the coefficient of $x^{10}$ and multiply it by $10!$ or find the coefficient of $\frac{x^{10}}{10!}$ in the expansion of $$\bigg( \frac{x^2}{2} + \frac{x^3}{3!} + ..\bigg) \times \bigg(1+x + \frac{x^2}{2} + \frac{x^3}{3!} + ..\bigg)^{25} $$
You can find the answer  by wolfram - alpha , so the answer will be the sum of the two condition such that $$\bigg[C(26,1) \times C(25,9) \times P(10,10) \bigg] + C(26,1) \times [x^{10}] \bigg[\bigg( \frac{x^2}{2} + \frac{x^3}{3!} + ..\bigg) \times \bigg(1+x + \frac{x^2}{2} + \frac{x^3}{3!} + ..\bigg)^{25} \bigg] $$
NOTE $2 =$ In my solution  , it is assumed that the particular letter must occur.
