A classroom contains 9 students. A student committee of 3 (president, vice-president, and treasurer) must be selected. Harry Potter will serve only as president and only if either of his friends Ron Weasley or Hermione Granger serve as vice president; otherwise he leaves the group. The others (including Ron and Hermione) have no such restrictions. What is the probability that Ron or Hermione become the president of this group? Report answer to 3 decimal places.

Question
Asked Jun 4, 2019

A classroom contains 9 students. A student committee of 3 (president, vice-president, and treasurer) must be selected. Harry Potter will serve only as president and only if either of his friends Ron Weasley or Hermione Granger serve as vice president; otherwise he leaves the group. The others (including Ron and Hermione) have no such restrictions. What is the probability that Ron or Hermione become the president of this group? Report answer to 3 decimal places.

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Step 1

Total number of students = 9

Student committee of three people with designations President, Vice-president and Treasurer is to be selected. 

Harry potter can be selected in committee as president or he leaves the group. So there are two cases that
1. Harry potter is president
2. Harry potter is not president, which means he leaves the group and there are only 8 students are to be considered to select the committee.

Step 2

Let us consider the first case where Harry potter is president. 
When harry potter is president then either Ron Weasly is Vice president or Hermione Granger is Vice president.So it has two cases as follows

Case-1
Harry Potter President and Ron Weasly vice president.
Here two spots in committee are taken and treasurer spot is left.
The total number of ways of selecting one treasurer among 7 students = 7P1 = 7

Case-2
Harry Potter President and Hermione Granger is  vice president.
Here two spots in committee are taken and treasurer spot is left.
The total number of ways of selecting one treasurer among 7 students = 7P1 = 7.

Step 3

Let us consider the case if Harry potter is not President then He leaves the group, so anyone except Harry Potter can be selected in committee.

While selecting three members in committe each one of the member have distinguished position. So we use Permuation h...

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