A classroom contains 10 students. A student committee of 3 (president, vice-president, and treasurer) must be...

A classroom contains 10 students. A student committee of 3 (president, vice-president, and treasurer) must be selected. Harry Potter will serve only as president 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?

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Expert Solution

Total number of ways:

Harry Potter will serve as president AND Ron will serve as vice president AND any one serve as treasurer is:

Harry Potter will serve as president AND Hermione will serve as vice president AND any one serve as treasurer is:

Harry Potter will not serve as president means any one except Harry Potter (remaining students 9) serve at three places:

Total number of ways = 8+8+504 = 520

Ron become the president of this group means anyone except Ron and Harry Potter (remaining students 8) serve at remaining two places:

Hermione become the president of this group means anyone except Hermione and Harry Potter (remaining students 8) serve at remaining two places:

Favorable cases when Ron or Hermione become the president of this group is:

Favorable cases = 56+56 = 112

The probability that Ron or Hermione become the president of this group is:

orchestra answered 11 months ago

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