(Answered) Math 10b quiz 1-1 explain why the following statement is

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Math 10B Quiz 1-

1. Explain why the following statement is true: For any positive integer n, the number of subsets of a set with n different elements is 2ⁿ.

2. We say that a string of five decimal digits is valid if it satisfies both of the following two conditions:

(i) At least one of the five digits is a "0".

(ii) The five digits are all distinct.

How many valid strings are there?

3. You are giving an exam in a classroom where 24 chairs are arranged in a circle. To discourage heating, you do not want students to sit next to each other. What is the maximum number of students that can take the exam in this room? Explain your answer carefully.

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