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? **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.

Name: This is a discrete math (counting techniques) problem. Please explain
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: 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 betwe

Given:- Let T = {0,1,2}. A string x ∈ T" is said to be balanced if the sum of the digits is an integermultiple of 3.1. Show a bijection between the set of strings in T 6 that are balanced and T 5. Explain why yourfunction is a bijection.2. How many strings in T 6 are balanced?Solution:- a) Consider a map which sends a string to its prefix that its length is = 5 This map will be a bijection as the obtained 5 digits tell if the next digit will be one of 0 , 1, or 2. b) The number of string balanced is given by 3 5 = 243.