There are (n + 1) white and (n + 1) black balls, each set numbered 1 to n + 1. The number of ways in which the balls can be arranged in a row so that adjacent balls are of different colours, is

Out of 15 balls, of which some are white and the rest are black, how many should be white so that the number of ways in which the balls can be arranged in a row may be the greatest possible? It is assumed that the balls of same color are alike?

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that at least one ball is separated from the balls of the same color.

Find the number of ways in which 5A^(prime)sa n d6B ' s can be arranged in a row which reads the same backwards and forwards.

There are n distinct white and n distinct black ball. If the number of ways of arranging them in a row so that neighbouring balls are of different colors is 1152, then value of n is _________.

Find the number of ways in which 5 distinct balls can be distributed in three different boxes if no box remains empty.

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from lot.

Ten identical balls are distributed in 5 different boxes kept in a row and labeled A, B, C, D and E. The number of ways in which the ball can be distributed in the boxes if no two adjacent boxes remains empty

Let theta=(a_(1),a_(2),a_(3),...,a_(n)) be a given arrangement of n distinct objects a_(1),a_(2),a_(3),…,a_(n) . A derangement of theta is an arrangment of these n objects in which none of the objects occupies its original position. Let D_(n) be the number of derangements of the permutations theta . There are 5 different colour balls and 5 boxes of colours same as those of the balls. The number of ways in which one can place the balls into the boxes, one each in a box, so that no ball goes to a box of its own colour is

Out of 10 white, 9 black, and 7 red balls, find the number of ways in which selection of one or more balls can be made (balls of the same color are identical).