In how many ways can the letters in the word DIFFUSION be rearranged?

Basagabi asked Feb 11, 2023

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Basagabi asked Feb 11, 2023

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23 votes

Solution

DIFFUSION

For this case we have a total of 9 words

1 D, 2 F, 2 I, 1S, 1O 1N

Then the number of ways:

$(9!)/(1!\cdot2!\cdot2!\cdot1!\cdot)=90720$
$(9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)/(2\cdot1\cdot2\cdot1)=(362880)/(4)=90720$

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