How Many Unique Circular Arrangements for the Word POTATOES?

Thread starter pivoxa15
Start date Jul 18, 2007

AI Thread Summary

To determine the unique circular arrangements of the letters in "POTATOES," the formula for circular permutations is applied, which is (n-1)!. The word contains 8 letters, with 'O' and 'T' each appearing twice. The initial calculation of 7!/(2!2!) yields 1260 arrangements. However, the expected answer is 150, indicating a miscalculation in accounting for identical letters in a circular arrangement. The discrepancy highlights the need for a more thorough analysis of the arrangements considering the circular nature and repetitions.

Jul 18, 2007

pivoxa15

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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Jul 18, 2007

chaoseverlasting

Seems right to me...

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