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.

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?

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.

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).

There are four balls of different colors and four boxes of colors same as those of the balls. Find the number of ways in which the balls, one in each box, could be placed in such a way that a ball does not go to box of its own color.

Find the number of ways of selecting 9 ball from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls fo each colour.

There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. Prove that the number of ways in which a man can choose at least one ball from each bag is^(2n)C_n-1.