Question

Let there are 4 red, 3 yellow and 2 green balls, then total number of arrangements in a row such that no two balls of same colour are together (balls of same colour are identical) are

Answer 1

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Answer 2

Answer:

The balls can be arranged in 1260 ways such that no two balls of same color are together

Step-by-step explanation:

Number of red balls = 4

Number of yellow balls = 3

Number of green balls = 2

To make sure that no two balls of same color can be together we place the 4 red balls and insert yellow and green balls between them.

Number of ways to insert 3 yellow and 2 green balls, total of 5 balls between 4 red balls that is at 3 places

⇒ arrange 5 balls in 3 places

$_{3}^{5}\textrm{C}=10$

Hence, The balls can be arranged in 10 ways such that no two balls of same color are together