There are 2 identical white balls, 3 identical red balls and 4 green balls of different shades. The number of possible ways in which they can be arranged in a row so that atleast one ball is seperated from the balls of the same colour is ?

Hi Student

The above can be solved as total cases minus the number of cases in which no ball is separated

Total cases- 9!/2!3! ( as green ball are of different shades they can be distinguished)
Number of cases in which all are together is by considering 2 while ball as one unit 3 red balls as one unit and 4 green balls as one unit is 3!

Required ways is 9!/2!3! – 3!