Let T = {0, 1,2}. A string x E T" is said to be balanced if the sum of the digits multiple of 3. an integer 1. Show a bijection between the set of strings in T6 that are balanced and T³. Explain why your function is a bijection. 2. How many strings in T6 are balanced?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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This is a discrete math (counting techniques) problem. Please explain clearly, no cursive writing.

 

Let \( T = \{0,1,2\} \). A string \( x \in T^n \) is said to be balanced if the sum of the digits is an integer multiple of 3.

1. Show a bijection between the set of strings in \( T^6 \) that are balanced and \( T^5 \). Explain why your function is a bijection.

2. How many strings in \( T^6 \) are balanced?
Transcribed Image Text:Let \( T = \{0,1,2\} \). A string \( x \in T^n \) is said to be balanced if the sum of the digits is an integer multiple of 3. 1. Show a bijection between the set of strings in \( T^6 \) that are balanced and \( T^5 \). Explain why your function is a bijection. 2. How many strings in \( T^6 \) are balanced?
**Additional Instructions**

For the exercises that ask you to answer "How many ...", express your results as a combinatorial formula, calculate the integer value that answers the question, and provide a short justification of your formula choice.
Transcribed Image Text:**Additional Instructions** For the exercises that ask you to answer "How many ...", express your results as a combinatorial formula, calculate the integer value that answers the question, and provide a short justification of your formula choice.
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