The coefficient of a5b6c7 in the expansion of (bc+ca+ab)9 is

(bc+ca+ab)9   =∑0≤r,s≤99!r! s! (9-r-s)!(bc)r(ca)s(ab)9-r-s =∑0≤r,s≤9 9! a9-rb9-scr+sr! s! (9-r-s)! For coefficient of a5b6c7 , we set 9-r=5,9-s=6,r+s=7⇒r=4,s=3∴ required coefficient is 9!4!3!2!=9×8×7×6×56×2=1260