Find the coefficient of x^25 in (1 +x +x^8)^10

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13-09-2019
Mathematics

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Find the coefficient of x^25 in (1 +x +x^8)^10

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LammettHash LammettHash · Answer 1 · 2019-09-13T18:19:58+02:00

LammettHash LammettHash

13-09-2019

The only way to get a term containing [tex]x^{25}[/tex] is to take 6 copies of 1, 1 copy of [tex]x[/tex], and 3 copies of [tex]x^8[/tex] (since 6+1+3=10, and 6*0+1*1+3*8=25). So this term has a coefficient of

[tex]\dfrac{10!}{6!1!3!}=840[/tex]

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