For the sake illustration lets say $n>5$ consider: $\displaystyle {(x + y)^n} = (x + y)(x + y)(x + y)\underbrace \cdots _{n - 5}(x + y)(x + y)$.

In going across that product we stop at term and take either $x\text{ or } y$ When done we have $k~x's~\&~j~y's$ and $k+j=n$

You have seen this idea played out many times. $xxxxxxxyyyy$ how many ways can those eleven be rearranged?

$\dfrac{11!}{7!\cdot 4!}=\dbinom{11}{7}=330$

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That is like stopping eleven times picking $7~x's~\&~4 y's$ in random order. That can be done in 330 ways.

Thus $330x^7y^4$ is in that expansion.

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Note the both $330x^7y^4~\&~330x^4y^7$ are terms in the expansion. Why is that?

In the expansion of $(x+y)^{21}$, what is the coefficient of the $x^{10}y^{11}$ term?