Find the total number of arrangements of the letters in the expression

When expanded, a3 b2 c4   would result in total 9 letters.

This is same as permuting 9 things, of which 3 are similar to the first kind, 2 are similar to the second kind and four are similar to the third kind, i.e. three as , two bs and four cs.

Required number of arrangements $=\frac{9 !}{3 ! 2 ! 4 !}=1260$