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Eight balloons (two blue, two green, two yellow, and two red) are randomly arranged in a line. Balloons of the same color are indistinguishable from one another. 

 

Find the total number of possible arrangements

Find the number of arrangements in which the first four balloons have different colors.

 Jul 2, 2021
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The number of total arrangements is 8!/4 * 2! = 8! / 8 = 7! = 5040. 

There are 5040 total arrangements.

 

The number of arrangements in which the first four balloons have different colors is 4! * 4! = 24 * 24 = 576. 

There are 576 total arrangements.

 

Hope this helped!!

 Jul 2, 2021

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