How Many Unique Circular Arrangements for the Word POTATOES?

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SUMMARY

The discussion centers on calculating the number of unique circular arrangements for the letters in the word "POTATOES." The correct formula for arranging n distinguishable objects in a circle is (n-1)!. Given that the letters O and T each appear twice, the calculation should be adjusted to account for these repetitions. The accurate computation is 7!/(2!2!) which results in 1260 arrangements, but the correct answer is 150, indicating an error in the initial approach.

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Homework Statement


In how many ways can the letters of the word POTATOES be arranged in a circle?


Homework Equations


n distinguishable objects can be arranged in a circle in (n-1)! ways.


The Attempt at a Solution


O and T both have two identical copies so it should be 7!/(2!2!)=1260

But the answers suggested 150.

Can't see where I made my mistake.
 
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