Question

What is the coefficient of x^5y^5 in the expansion of (x+y)^10

Answer 1

252

Explanation:

We know the binomial expansion of

`(a + x)^(n) = a^(n) + C_(1)a^((n - 1)) x + C_(2) a^((n - 2)) x^(2) + ........ + C_(r) a^((n - r)) x^(r) + ........ + x^(n)`

Therefore, in the binomial expansion of
`(x + y)^(10)` the term with
`x^(5)y^(5)` expression will be there when r = 5

Hence, the term will be
`^(10)C_(5) x^(5) y^(5)`.

Therefore, the coefficient of
`x^(5)y^(5)` will be

`^(10)C_(5) = (10!)/(5! * 5!) = 252` (Answer)