how to find the coeff

let powers of ab,bc and ca, be x,y,and z..
we have (ab)^x(bc)^y(ca)^z=a³b⁴c⁵
we have x=1, y=3,z=2
now we have say 6 brackets,
of the type (l+m+n) multiplied wid each other..
so we need frm here the coeff of lm³n²
for this out of the six brackets we have to chose 1 bracket dat wud contribute an l, can be donw in 6 ways,
then out of the 5 remaining brackets we choose 3 brackets dat wud contribute an m, which can happen in ⁵C₃ways
and the remaining 2 brackets will contribute an n each..
so we have the coeff as
6*⁵C₃*1
cheers!!!