Question

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

Answer 1

The only way to get a term of degree 25 is by taking 3 copies of
`x^8`, 1 copy of
`x`, and 6 copies of 1. Then the coefficient of
`x^(25)` is

`\dbinom{10}3\dbinom71\dbinom66=\dbinom{10}{3,1,6}=(10!)/(3!6!)=\boxed{840}`