There are 3 blue balls, 4 red balls and 5 green balls.
Question:

There are 3 blue balls, 4 red balls and 5 green balls. In how many ways can they are arranged in a row?

 

Solution:

To find: no of ways in which the balls can be arranged in a row where some balls are of the same kind

Total number of balls $=3+4+5=12$

3 are of 1 kind, 4 are of another kind, 5 are of the third kind

Number of ways $=\frac{12 !}{3 ! 4 ! 5 !}=27720$

They can be arranged in 27720 ways

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