Question

How many ways are there to rearrange the letters in the word potato, not including indistinguishable rearrangements?

Answer 1

$\dfrac{6!}{2!2!}=\dfrac{3\cdot4\cdot5\cdot6}{2}=180$

Answer 2

The number of ways to arrange the words, not including indistinguishable rearrangements is 180ways.

Given the word POTATO, to determine the number of ways is there to rearrange the letters, not including indistinguishable rearrangements, this is expressed as:

$N=\frac{T}{r!r!}$

where T is the total number of letters in "POTATO"

r is the number of letters that are repeated

From the given word count;

T = 6

r = 2

Substitute the values into the formula as shown:

$N=\dfrac{6!}{2!2!}\\N=\frac{6\times5\times4\times3\times2!}{2!2!}\\N=\frac{360}{2}\\N=180$

Hence the number of ways to arrange the words, not including indistinguishable rearrangements is 180ways.

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