Eight$-$queens problem Consider the classic puzzle of placing eight queens on

an $8\backslash$times $8$ chessboard so that no two queens are in the same row or in the same

column or on the same diagonal. How many different positions are there so

that

a$.$ no two queens are on the same square?

b$.$ no two queens are in the same row?

c$.$ no two queens are in the same row or in the same column?