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 .

You are given 8 balls of different colour (black,white ......). The number of ways in which these balls can be arranged in a row so that the two balls of particular colour (say red and white) may never come together is-

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.