Find the number of ways of selection of one or more letters from AAAABBCCCDEF if the letters A B are selected atleast once

the given letters are 4 A , 2 B , 3 C , 1 D , 1 E, 1F.
4 A can be chosen in 4 ways, either we choose 1 A or 2 A or 3 A or 4 A.
2 B can be chosen in 2 ways, either we choose 1 B or 2 B
3 C can be chosen in 4 ways , either we choose 1 C or 2 C or 3 C or we do not select C.
similarly 1 D can be chosen in 2 ways. 1 E and 1 F can be chosen in 2 ways each.
therefore the number of ways of selection (such that A and B are selected at least once)
= 4*2*4*2*2*2
= 256 ways

hope this helps you