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In a classroom, there are 8 desks equally arranged in two columns (i.e. each column has four desks). Each desk can accommodate 2 people and there are eight boys and eight girls in total. When two opposite genders share a desk, we call them group 1 and when two same genders share a desk we call them group 2.

The following is one possible way of sharing the desks, where O represents male, + represents female and -- represents the desk

O+   O+
--   --

OO   OO
--   --

O+   ++
--   --

O+   ++
--   --

Now the question is, what is the percentage of group 1 in first and second column?

For the first column, I would count the frequency of group 1 (i.e., 3) and divide it by total number of pairs present in the classroom (i.e., 8) and multiple it with 100, which would give me 37.5%. Hence as per my calculation, I would say that there are 37.5% of group 1 in the first column and 12.5% of group 1 in the second columns.

Am I doing it right? If not, please let me know the correct way of calculating the percentage of group 1 for each column?

Daddy_enakku_oru_doubt
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  • Writing the rows as columns is confusing. There are 4 desks in group 1, 3 of them are in row 1, so the percentage in the first row is 75%. – almagest Apr 19 '16 at 13:04
  • Was this really the answer you were looking for? Considering you writing "The following is one possible way of sharing the desks" then the answer to your question is completely different. – JKnecht Apr 19 '16 at 13:29
  • @almagest My bad.. Thank you for pointing out the typo. Now, does that mean that I have 62.5% (i.e., 5/8) of males in column one? – Daddy_enakku_oru_doubt Apr 19 '16 at 14:00
  • @JKnecht Yes, As I had mentioned, the above is just one possible way of sharing the desks and the percentage should change as per different arrangements. Can you please help me understand, how will that change the answer? Are you talking about creating an expression for the above? – Daddy_enakku_oru_doubt Apr 19 '16 at 14:03

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