Question 1185953
.
<pre>

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  {{{14!/(9!*5!)}}} = {{{(14*13*12*11*10)/(1*2*3*4*5)}}} = 2002  ways.
</pre>

Solved.


---------------


On distinguishable permutations/arrangements, &nbsp;see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Arranging-elements-of-sets-containing-undistinguishable-elements.lesson>Arranging elements of sets containing indistinguishable elements</A> 

in this site.