Problem Statement
Having three black objects B and one white object W they can be grouped in 7 ways like this:
(BBBW)
(B,BBW)
(B,B,BW)
(B,B,B,W)
(B,BB,W)
(BBB,W)
(BB,BW)
In how many ways can $3N^2$ black objects B and $2N^2$ white objects W be thus grouped? Give your answer mod $1\,000\,000\,007$.
Submit Answers
You need to submit in the format: "N:problem(N)", possibly with multiple values at once, separated by commas, with $N$ between $1$ and $100$.