There are $N$ vertices of the 24-cube which have a 1 in the $i$th coordinate and a total of five 1s.
We adopt the convention that the first coordinate $i$ increases as one goes downwards, and the second coordinate $j$ increases as one goes from left to right.
Now $X$ can be taken as coordinate variable on $M$.
This explains why we chose 9 rather than, say, 1 for the second coordinate.
Keep only those vertices whose coordinates sum to 4.
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