Prove that the number of ways in which n books can be placed on a shelf when two particular books are never together is `( n-2) xx (n-1) !`

Number of ways in which 15 different books can be arraged on a shelf so that two particular books shall not be 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

In how many ways can 12 books be arranged on a shelf if 4 particular books must always be together.

The number of ways in which seven persons can be arranged at a round table if two particular persons may not sit together, is

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

In how many ways can 20 books be arranged on a shelf so that a particular pair of books shall not come together?

There are 6 books of physics , 3 of chemistry and 4 of biology . Number of ways in which these bokks be placed on a shelf if the books of the ame subject are to be together is

Show that the number of ways in which p positive and n negative signs may be placed in a row so that no two negative signs shall be together is (p+1)C_n .

Ten different books are arranged on a shelf . Find the number of different ways in which this can be done. If two specified book are (a) to be together, (b) not to be together.

There are 10 different books in a shelf. The number of ways in which three books can be selected so that exactly two of them are consecutive is