Combinations with a certain number of symbol repetitions

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Help please formulate a formula for calculating the number of all possible combinations for these conditions:

  • The string must contain the a certain number of characters (no more, no less )!
  • Symbol A - 2 count
  • Symbol B - 3 count
  • Note: characters and their count can be more than two (for example, C-1, D-2, E-32, etc)

I sketched all the combinations manually for an example:

aabbb
abbba
bbbaa
bbaab
baabb
abbab
ababb
babba
babab
bbaba