Equality involving binomial coefficient

Question

I think the following equality is correct, but I'm not sure, so I'm asking you: $$\left(\prod_{\large\tfrac{n}{2}\,<\,p\,\le\,\tfrac{6n}{7}}p\right)\cdot\left(\prod_{\large n\,<\,p\,\le\,3n\strut}p\right)<\binom{3n}{\frac{n}{2}}$$ for even $ n $. $ p $ is a prime.

Is $p$ representative of a prime, or a generic integer? – abiessu Jul 26 '15 at 16:49 — abiessu, Jul 26 '15 at 16:49
Oh, sorry , I forgot:$ p $ is a prime ;D – marcin2345 Jul 26 '15 at 16:50 — marcin2345, Jul 26 '15 at 16:50

score 0 · Answer 1 · answered Jul 26 '15 at 16:54

0

Not correct.

For $n=4$, $$1155=3\cdot (5\times 7\times 11)\color{red}{\gt} \binom{12}{2}=66.$$

answered Jul 26 '15 at 16:54

mathlove

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Equality involving binomial coefficient

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