find the generating function for the number of

Question

Find the generating function for the number of r-combinations of {3.a, 5.b, 2.c}         

Ans:  Terms sequence is given as r-combinations of {3.a, 5.b, 2.c}. This can be written or illustrated as ^rC_3.a, ^rC_5.b, ^rC_2.c. Now generating function for this finite sequence is given by 

f(x) = ^rC_3.a + ^rC_5.bx + ^rC_2.cx²