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GATE CSE 2025 Session 1 Q30: Ternary strings of length 5 with a repeated adjacent symbol

Question

Let SS be the set of all ternary strings defined over the alphabet {a,b,c}\{a, b, c\}. Consider all strings in SS that contain at least one occurrence of two consecutive symbols, that is, "aa", "bb" or "cc". The number of such strings of length 5 that are possible is _______. (Answer in integer)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 195 (official GATE 2025 final answer key)

Concept used: Complementary counting: count strings with no two equal adjacent symbols and subtract.

First step: Strings with no equal neighbours: 3 choices for the first symbol and 2 for each later one, i.e. 3⋅243 \cdot 2^4; subtract from 353^5.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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