It's much better to just attach a picture:
It would also help if you would put this in context. What problem are you trying to solve?
When you ask for the "rationale for using a matrix", what do you mean? I see no indication of a matrix, though I initially supposed (because of that question) that those are column vectors, rather than binomial coefficients, as they in fact are.
If you didn't realize that, the way to evaluate this is to use the nCr button on your calculator.
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