1.

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

Answer» Number of ways balls are arranged in a row so that at least one ball is separated from the balls of same colors,
= Total Number of ways - All identical balls together
Total number of ways balls can be arranged `n(S) = (9!)/(2!3!)`
`n(S) = (9!)/12 = (9**8**7!)/12 = 6 (7!)`
The number of ways balls are arranged so that identical balls are together `n(T) = 3!4!`
So, the number of ways balls are arranged so that at least one ball is separated ` =n(S) - n(T) = 6 (7!) -3!4! = 6 (7!) -64! = 6(7!-4!)`


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