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You are making a string of coloured balloons as a decoration for the formal. If you have five green, six gold, and four white balloons, in how many ways can you arrange them along the string?

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  1. There are 15! ways to arrange the balloons. But, the 5 green balloons can be rearranged in 5! ways that appear the same. Same thing for the other colors. So, you end up with

    15!/(5!6!4!) = 630,630 ways

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