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If $3$ dice are thrown together the no. of ways in which the sum of numbers appearing on the dice is $n$, is? $ \ $ $9 \leq n \leq14$

My try: $(x^1+x^2+x^3+x^4+x^5+x^6)^3$

The sum of the coefficients of $x^9$ to $x^{14}$ should be found. But I am getting stuck up in calculations. Now I have started doubting this method.

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    Clarifying your question... You seek the total number of ways to roll three dice and get sums of 9 through 14, inclusive. Correct? – 2017-02-23
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    Yes,you got it right. – 2017-02-24
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    Your approach should work. Please show your efforts. – 2017-02-24

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