A fiveperson committee composed of Diane Todd Princess Carol

A five-person committee composed of Diane, Todd, Princess Carolyn, Mr. Peanut Butter, and BoJack is to select a chairperson, secretary, and treasurer. How many selections are there in which at least one office is held by Todd or Diane? Assume that each person can hold at most one office.

Solution

There are total of 3 positions to be filled from five candidates

Number of ways to select 3 people from 5 people = 5C3 = 10 ways

Number of Occurences when both Todd and Diane are not part of organization = 3C3 = 1 ways

Hence number of ways of selecting = 10 - 1 = 9 ways