# Find number of ways of selection of one or more letters from the word: AAAABBCCCDEF

the answer is 479 but how does it come?

As $A$ occurs $4$ times, we can choose A in $4+1$ ways
So, the number of ways of selection of no or more letters from the word: AAAABBCCCDEF will be $N=(4+1)(2+1)(3+1)(1+1)(1+1)(1+1)$
So, the number of ways of selection of one or more letters will be $N-1$