Problem - 4480
Let $n$ be a positive integer. Find the number of ordered collection of integers $(a,\ b,\ c,\ d)$ such that $1\le a < b \le c < d\le n+1$
The collections $(a,\ b,\ c,\ d)$ and $(a,\ b,\ c+1,\ d+1)$ have a bijection. Meanwhile, choosing $(a,\ b,\ c+1,\ d+1)$ is equivalent to selecting $4$ elements from $(n+2)$ elements from $1$ to $(n+2)$, inclusive. Therefore, the answer is $$\boxed{\binom{n+2}{4}}$$