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Q.

A four digit number is called a doublet if any of its digit is the same as only one neighbour. (For exampel, 1221 is doublets but 1222 is not), Number of such doublets are

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answer is 2268.

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Detailed Solution

Case–1 abbc
We can choose a in 9 ways, b in 9 ways, and c in 9 ways. Hence, there are 93 possibilities for this case.

Case–2 bbac
There are 9 possibilities for b, and 9 possibilities for each a and c. Once again, we have that there are 93 possibilities for this case.

Case – 3 acbb
Once again, there are 9 possibilties for a and c, and 9 possibilties for b. hence, these are 93 possibilities for this case.
Case – 4 aabb
We have 9 possibilities for a and 9 possibilities for b. We thus have 81 possibilities for this case. We can now sum up our answers, to get a total of

3.93+81=2268 total ways 

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