Find the number of rearrangements of the string 11223344 that contain no two consecutive equal digits(adsbygoogle = window.adsbygoogle || []).push({});

So for the total rearrangements we have

[itex]\stackrel{8!}{2!2!2!2!}[/itex]

I was thinking I would count the total number of rearrangements that have the same digit next to each other

So I started with the total number of rearrangements and sub tract the number of rearrangements that share the same number with the first number selected

[itex]\stackrel{7!}{2!2!2!}[/itex](4) I multiplied by four because there are 4 numbers. From here I am confused, do you assume that you have had 2 digits in a row or do you assume you could have any rearrangement of the 6 digits?

Im thinking the last term would be 4!, im not sure of the sign though

So far I have

[itex]\stackrel{8!}{2!2!2!2!}[/itex]-[itex]\stackrel{7!}{2!2!2!}[/itex](4)+............. 4!

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# Rearrangement of 11223344

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