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Prove that \(\displaystyle \prod _{ r=0 }^{ a } \binom{a}{r} =\left(\prod _{ r=0 }^{ b } \binom{b}{r} \right)\left(\prod _{ r=1 }^{ a-b }{ \frac { { (b+r) }^{ b+r-1 } }{ (b+r-1)! } }\right )\) , where \(a>b\).

I had previously posted this as a question which hadn't got much response so I am now posting this as a note.
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Note by Abhishek Sharma
2 years ago

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Can I mention really quickly that in this problem, you didn't specify that the brackets meant the floor function? To avoid ambiguity, write \(\lfloor x\rfloor\) (code: \lfloor x\rfloor) instead of \([x]\). (P.S. How do you do a private message here?) Akiva Weinberger · 2 years ago

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@Akiva Weinberger My bad. I have corrected it now. Abhishek Sharma · 2 years ago

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