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> Find the coefficient of $x^{25}$ in $(1 + x^3 + x^8)^{10}$.
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Here is my solution I am looking to see if it is correct or if there is another way to do it, thanks!

The only way to form an $x^{25}$ term is to gather two $x^8$ and three $x^3$ . Since there are ${{10}\choose{2}} =45$ ways to choose two $x^8$ from the $10$ multiplicands and $8$ ways to choose three ${{8}\choose{3}}= 56$ ways to choose $x^3$ from the remaining $8$multiplicands, the answer is using the product rule $45×56 = 2520$.