IIT JEE , AIEEE Forum - Mathematics , Algebra

navi

two squares are choosen at random on a chess board.then show that probability that they hav a side in common is 1/18.

ramyadiamond

i'm just explaining the method here.

Considering two blocks row-wise and coloumn wise, u'll see that a pattern is formed as u move down the board, so detect the pattern of the two blocks that share a side, add them up and to find the probability, divide it by 64C2.

I hope its right. Plz tell me if you haven't understood.

rik_mad

two squares can be chosen in 64c2 ways

along a particular row since there are 8 squares the no of ways we can choose two consecutive squares is 7 there re 8 rows so total ways 56

similarly for 8 columns

so probanility is

2(56)/(64c2)

= 1/18

iitkgp_bipin

Two squares have same side if they are in the same row or same column and thay are adjacent.
7 such pairs are possible along a row and there are 8 such rows gives 8*7=56 pairs.
Similarly 56 pairs are possible for 8 columns.
Hence total no. of possible pairs = 56 + 56 = 112

2 squares can be choosen in ⁶⁴C₂ ways.

Hence required probability = 112/⁶⁴C₂ = 1/18

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