(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2 squares are chosen at random from a chess board.What is the chance that these 2 squares will share exactly 1 corner?

2. Relevant equations

P=favourable possibilities/Total possibilities

3. The attempt at a solution

So,the total no of possibilities should be 64C2.

Now,for favourable...

For the 4 corners,only 1 square is possible,so 4 cases.

For one side(excluding the corners) there can be 2 squares for every square we choose.,i.e

6×2=12 cases in on side...48 cases for all sides.

Now,we are done with the borders and are just left with the middle ones.

For each middle one there can be 4 possible squares..i.e,

36×4=144 cases

Summing up,we get P=(4+48+144)/64C2

=196/64C2

Is this correct or have i missed (or added) something?

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# Homework Help: Chess board probability

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