The number of ways of arranging `n(gt2)` distinct objects in a line so that two particulars objects are never together is

The number of ways of arranging m white and n black balls in a row (mgtn) so that no two black are placed together, is

The number of ways of arranging m white and n black balls in a row (mgtn) so that no two black are placed together, is

Let N denote the number of ways in which n boys can be arranged in a line so that 3 particular boys are seperated then N is equal to

Let N denote the number of ways in which n boys can be arranged in a line so that 3 particular boys are seperated then N is equal to

The number of ways in which n books can be arranged on a shelf so that two particular books are not together is

Show that the number of ways in which n books may be arranged on a shelf so that two particular books shall not be together is (n-2)(n-1)!