Find the number of ways in which onee or more letters can be selected from the letter.
AAAAA BBBB CCC DD EFG.

Explanation

here, 5A's are alike, 4B's are alike, 3C's are alike, 2D's
`therefore` Total number of combinations
`=(5+1)(4+1)(3+1)(2+1)2^(3)-1`
`=6*5*4*3*8-1`
`=2879`
[excluding the base, when no letter is selected]
Explanation selection from (AAAAA) can be made by 6 ways such include no A, include five A. similarly, selections from (BBBB) can be made in 5 ways, selections from (CCC) can be made in 4 ways, selections from (DD) can be made in 3 ways and form E,F,G can be made in `2xx2xx2` ways.