similarly, for rest of the questions make cases from the diagram. Post the specific cases that you have made for any one answer you're not getting and someone shall chip in!
I particularly need explaination of Q5. In how many ways can two 1cm x 1cm black squares be selected in a 8cm x 8cm chessboard/grid such that they are not in the same row or same column?
you may get to the answer by eliminating options itself. only 400 seems close to the answer (it has to be greater than 32 - because that is the number of black squares on the board. right?)
anyhow, the solution:
number of black squares on the board = 32 (4 in each of the 8 rows - 4 in each of the 8 columns)
ways of selecting 1 black square out of 32 = 32
that makes us exclude 7 black squares for our next selection (3 each from the row and the column we picked our first black square and that selected black square itself)
hence, ways of selecting the second black square = 32-7=25
so total ways = 32x25=800
now because the 2 black squares are identical, you have counted them twice in your calculation. you have counted cases for the same pair where a black box was considered first selection and was considered the second selection separately.
we want selection and not permutation, so divide by 2. you get 400.
did that help?