a chessboard is and 8X8 arrangement of 64 squares suppose ei

a chessboard is and 8X8 arrangement of 64 squares. suppose eight chess pieces are placed on a chessboard at random so that each square can receive at most one piece. what is the probability that there will be exactly one piece in each row and in each column?

show steps plz!

Solution

To simplify the analysis, wesay that the pieces are pawns, so that the order would not matter.

Thus, there are 64C8 = 4426165368 ways to choose locations.

Say we put the pieces one by one, for each column, from left to right.

For the first piece has 8 options.

As there\'s only one piece per row, the second piece only has 7 options.

Continuing the trend, the third has 6 options, fourth has 5 options, fifth has 4 options, sixth has 3 options, seventh has 2 options, and 8th has 1 option.

Hence, there are 8*7*6*5*4*3*2*1 = 40320 ways to do the task.

Thus, the probability is

P = 40320/4426165368 = 0.00000910947 [ANSWER]