How many word can we make with infinited times of $B$, $D$ $M$ and only one $O$?

Question

In a case, we have infinite times of the letter B, D, M and only one O. How many different word containing those letter can we make (can be meaningless in this term) ?

Answer 1

As you have infinite letters of at least 2 types you can make infinite words. Example:

B, BD, BBD, BBBD, ...

If you mean words with length n:

Denote the ways to make a word with infinite B,D,M and length k by G(k).Then the answer you need is G(n) + n * G(n-1).

To find G(n), let's say the word is _ _ _ ... _ _ _. Then each blank can be B, D or M so G(n) = 3^n

Therefore You can make 3^n + n * 3^(n-1) words with length n with infinite B, D and M and 1 O