Find the number of ways to distribute 6 black hats and 6 white hats among four students $\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D }$ according to the following rules without remainder. (Note: hats of the same color are not distinguished from each other.) [4 points]\\
(가) Each student receives at least 1 hat.\\
(나) The number of black hats each student receives is different from one another.