How many strings of length 9 over the alphabet {a, b, c} are there which contain at least seven consecutive a’s? Hint: Upon writing down a few such strings you will notice that they must take one of three distinct forms (depending on where the consecutive a’s are). Then use the inclusion–exclusion principle.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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How many strings of length 9 over the alphabet {a, b, c} are there which contain at least seven consecutive a’s?

Hint: Upon writing down a few such strings you will notice that they must take one of three distinct forms (depending on where the consecutive a’s are). Then use the inclusion–exclusion principle.

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