There are 20 people in a club. In how many ways can the club elect a president, a secretary and a treasurer, on person can hold more than one office?
Think of the case of 4 people for 3 different posts, and if any one person can hold zero, one, two or three posts.
There are 4 choices for the president, 4 choices for the secretary, and 4 choices for the treasurer. Invoking the multiplication rule, there is a total of 4×4×4=64 possible ways to choose the three posts.
Can you now extend the situation to 20 people?
1140
To find the number of ways in which the club can elect a president, a secretary, and a treasurer, taking into account that one person can hold multiple offices, we can multiply the number of choices for each position.
Let's break it down step by step:
1. For the president: Since all 20 people are eligible for this position, there are 20 possible choices.
2. For the secretary: Again, any of the 20 people can be chosen, including those who are already serving as president. Therefore, there are another 20 possibilities.
3. For the treasurer: Similarly, all 20 individuals are eligible, resulting in 20 choices.
To calculate the total number of ways, we multiply the numbers of choices together:
20 choices for the president × 20 choices for the secretary × 20 choices for the treasurer = 20 × 20 × 20 = 8,000
Therefore, there are 8,000 different ways in which the club can elect a president, a secretary, and a treasurer, with the possibility of one person holding multiple offices.