A hint to get started
Separate fixed digit counts from adjacent-repeat complements
A student working on a coding project studies 11-digit quaternary sequences. A quaternary sequence is a sequence formed using the digits 0, 1, 2 or 3. Examples are 12030201131, 01122211100, 12321232123 and 00000000000. Find the number of ways that 11-digit quaternary sequences can be formed with
(i) no restriction, mark
(ii) exactly four 0 s and four 2 s, marks
(iii) at least two consecutive digits that are the same. marks
[2017/PJC/II/9]
CJC · Review problems · Question 2
For an adjacent repetition, count the complement with every adjacent pair different.