Counting problem with a few restrictions (combinatorics)

Let's take Keno for example:

From number 1 to 80, there are $\dbinom{80}{20} = 3,535,316,142,212,174,320$ ways the casino can draw 20 numbers out of 80.

Given that the sum of the 20 numbers drawn is $n$ , how many combinations satisfy the following conditions:

$x_1+x_2\ldots+x_{20} = n$
$x_1,x_2,\ldots,x_{20}$ are distinct
$1 \leq x_i \leq 80$

Eg. If $n = 210$ , which is the minimum sum, $1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20 = 210$ , therefore there is only one possible combination for the sum of 20 numbers to be 210.

What about, say, $n = 896$ ? I have tried stars and bars but not really sure how to apply the distinct restriction.

#Combinatorics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$