Simple...
multiplying your binomial you get a GREAT number..but....I will only list a few..and I will give you the fourth term you seek...
\(e^{10} + 20e^{9} f+ 180e^{8} f^{2} +960e^{7} f^{3} +3360 e^{6} f^{4}\)....(etc)
As you can see...the forth term is \(960 e^{7} f^{3}\)
Thud, your answer.