Find the generating function, Mathematics

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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 rC3.a, rC5.b, rC2.c. Now generating function for this finite sequence is given by 

f(x) = rC3.a + rC5.bx + rC2.cx2


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