SOLUTION: In how many distinguishable ways can 5 identical black balls and 9 identical blue balls be arranged in a 2 x 7 array

It is OBVIOUS, that there is a one-to-one correspondence between distinguishable arrangements of 14 balls in line

and in a 2 x 7 array.



So, the problem is EQUIVALENT to ask 


        "In how many distinguishable ways can 5 identical black balls 
         and 9 identical blue balls be arranged in a line ?"


The formula and the answer are


    in   =  = 2002  ways.