Question

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

Answer 1

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

`(10!)/(6!1!3!)=840`