The number of 7letter words that can be formed using letters from A to G which neither contains the set CAD , BEG.

total no. of words that can be formed using A to G = 7p7 = 7!
taking CAD as a single element, the no. of words containing the set is = 5! (the 5 elements can be arranged in 5p5 ways)

similarly going for the set BEG , no. of words = 5!

hence total no. of words = 7! - 2(5!) = 4800