1. Math
  2. Advanced Math
  3. with clear steps and explanation please...

Question: with clear steps and explanation please...

Question details
With clear steps and explanation please
4. Two students are working on a problem that asks them to count 3-digit strings using 0-9, with repetition allowed, where at least one of the digits is a 1. Unfortunately, each student has an error in their reasoning. The first student says, My answer is 300. I used the Additive Principle. I let set A to consist of those strings where the first digit is 1 such as 123 or 145. Set B consists of those with the second digit equal to 1, and set C consists of those with the third digit equal to 1. Since at least one digit has to equal 1, AUBUC gives me the answer. To find the number of elements in A, I found that there are 10 possible options for each of the second and last digits, so there are a total of 100 elements in A. Similarly 100 elements in B and 100 elements in C. Therefore, by Additive Principle a) - 100+100+100 so the answer is 300. Does Student 1 undercount the set of 3-digit strings or overcount the set? Explain. b) The second student says, I counted 243. I also used the Additive Principle and the union, but I defined my sets differently. My set A consists of those strings where the first digit is 1 but the other digits are not 1. Similarly B includes strings where the middle digit is 1 and the others are not, and C includes those with the last digit equal to 1 and the other digits are not. I found each set to contain 81 elements for a total of 243 elements in all three sets. Does Student 2 undercount or overcount the set? Explain. Choose one of the students above who counted incorrectly, and modify their approach to count the set of 3-digit strings accurately. c)
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution