Question 1178272: There are 3 ABC branches in a city. The branches are called A, B, and C. Someone plans a 5-day visit to the city and wants to visit each branch. She/He will visit one branch per day, which means that the person will visit one or more branches more than once, possibly on consecutive days. How many different schedules can the travel advisor prepare for him/her? One possible schedule is A-B-B-C-A, where the person visits branch A on the first and fifth days, branch B on the second and third days, and branch C on the fourth day.
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
In order for successfully solve the problem, you should be able to re-formulate this many-words description
in compact form.
The number of all possible SCHEDULES is the number of all words of the length 5 (5 days in a week) written in 3-letter alphabet A, B, C.
It is the required re-formulation.
As soon as you re-formulated it, the answer  = 243 must be clear to you.
ANSWER. There are = 243 different possible schedules.
Solved and explained in all details.
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If you want to see many other similar (or different) problems, look into the lesson
- Combinatoric problems for entities other than permutations and combinations
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Combinatorics: Combinations and permutations".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
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