At a table in restaurant six people ordered roast beef three

At a table in restaurant six people ordered roast beef, three ordered turkey,two ordered pork chops, and one ordered flounder. of course no two portions of any of these items are absolutely identical the 12 servings are brought from the kitchen

in how many ways can they be distributed so that everyone get the correct item?

in how many ways can they be distributed so that no one can get the correct item?

Solution

a) 1!2!*3!*6! or (12-11)!(12-10)!(12-9)!(12-6)!

b)
12!/((6*3*2*1)4!)-(750*4(6+3+2+1));