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How many r-digit ternary sequences are there in which...

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How many r-digit ternary sequences are there in which:

A) No digit occurs exactly twice?
B) 0 and 1 each appear a positive even number of times?

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Solution Summary

R-digit ternary sequences are investigated. The solution is detailed and well presented.

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Please see the attached file for the complete solution.

How many r-digit ternary sequences are there in which
A) No digit occurs exactly twice?

Solution:
Let an denote the number of ternary string of length 4 with no pairs of adjacent digits like 00's, 11's and 22's.
So, if the first digit is 0 or 1, ...

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