- #1
Tanishq Nandan
- 122
- 5
Homework Statement
2 squares are chosen at random from a chess board.What is the chance that these 2 squares will share exactly 1 corner?
Homework Equations
P=favourable possibilities/Total possibilities
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?