1The number of ways of choosing the first square is 64. The number of ways of choosing the second square is 63. There are a total of 64 * 63 = 4032 ways of choosing two squares.
If the first square happens to be any of the four corner ones, the second square can be chosen in 2 ways. If the first square happens to be any of the 24 squares on the side of the chess board, the second square can be chosen in 3 ways. If the first square happens to be any of the 36 remaining squares, the second square can be chosen in 4 ways. Hence the desired number of combinations = (4 * 2) + (24 * 3) + (36 * 4) = 224. Therefore, the required probability = 224/4032=1/18
19total ways of selecting the squares =64*63
if first square is in one of the four corners, the second square can be chosen in just two ways
....total ways of selecting the sq here= 4*2=4ways
if first square is in one of the 24 non corner squares along the sides, the second square can be chosen in 3 ways
...total ways of selecting the sq here=24*3=72ways
if the if first square is in any of the remaining 36 squares, the second square can be chosen in 4 ways
...total ways of selecting the sq here=36*4=144ways
favorable ways= 224
probability = 1/18
62another method could be
no of ways of chosing 2 adjacent squares= 2x7x8
No fo ways of chosing 2 squares = 64x63/2
probability of event= 16x7/(32x63) = 1/18
19
Debotosh..
·2009-11-29 21:49:41
oops...i misread the question...i thought the qs asked for a corner in common !
62
Lokesh Verma
·2009-11-30 00:44:17
see any two squares will be adjacent along a line..
so there are 7 in each row..
there are 8 rows
and similar in each column..
hence 2x(7x8)
