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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 $$a>b$$.

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Note by Abhishek Sharma
1 year, 6 months 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?) · 1 year, 5 months ago