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how many distinguished arrangements are possible from a bag of 5 yellow eggs, 4 green eggs,...

how many distinguished arrangements are possible from a bag of 5 yellow eggs, 4 green eggs, 2 blue eggs, and 1 gold eggs?  

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Answer #1

There are total 5+4+2+1 = 12 eggs

these can be arranged in 12! ways

as 5, 4 and 2 items are identical

total possible arrangments are 12!/(5! * 4! * 2!) = 83160

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