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

Question 1185953: In how many distinguishable ways can 5 identical black balls and 9 identical blue balls be arranged in a 2 x 7 array
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.


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.

Solved.

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On distinguishable permutations/arrangements, see the lesson
- Arranging elements of sets containing indistinguishable elements
in this site.

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