If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+\ldots \ldots \ldots . .+...
If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+\ldots \ldots \ldots . .+C_{n} x^{n} \), prove that
\( \mathrm{P} \)
\[
C_{0} C_{3}+C_{1} C_{4}+\ldots \ldots \ldots+C_{n-3} C_{n}=\frac{(2 n) !}{(n+3) !(n-3) !}
\]
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