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by winnerhere » Fri Jun 18, 2010 8:47 am
In how many ways is it possible to select two white squares so that they lie in the same row or same column on a 8 x 8 Chessboard

1)12

2)48

3)96

4)60

5)100
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by tpr-becky » Fri Jun 18, 2010 8:56 am
you need to find out how many are available for the first pick - 8*8=64 squares - and 1/2 of them are white so there are 32 white squares. So for the first piece there are 32 ways to pick the first piece - then for the second piece there are 3 additional whites in each row and 3 additional whites in each column for 6 total pieces you could pick.

you multiply 32 *6 to get 192. Now because order doesn't matter you must divide by the number of pieces you are picking factorial (to eliminate all of the combinations that are essentially the same) - you are picking 2 pieces so you divide 192 by 2! - which is 96. Answer C.
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by winnerhere » Fri Jun 18, 2010 7:38 pm
tpr-becky wrote:you need to find out how many are available for the first pick - 8*8=64 squares - and 1/2 of them are white so there are 32 white squares. So for the first piece there are 32 ways to pick the first piece - then for the second piece there are 3 additional whites in each row and 3 additional whites in each column for 6 total pieces you could pick.

you multiply 32 *6 to get 192. Now because order doesn't matter you must divide by the number of pieces you are picking factorial (to eliminate all of the combinations that are essentially the same) - you are picking 2 pieces so you divide 192 by 2! - which is 96. Answer C.
Thanks Becky. I was getting 192 as answer and wondering !
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