Leila, Larry, and Cindy are running for 12th grade class offices. They will be named to the positions of president, vice-president, and secretary according to the number of votes each receives. The person with the most votes will be president, the person with the second-highest number of votes will be vice-president, and so on. In how many different ways can the three students form a set of class officers?
a.
5
b.
27
c.
6
d.
9
Is it 6?
You are correct.
6, yes.
To determine the number of different ways the three students can form a set of class officers, we need to consider the three positions: president, vice-president, and secretary.
First, let's identify the number of possibilities for each position:
1. President: There are three candidates (Leila, Larry, and Cindy) vying for this position. So, there are 3 possible choices for the president.
2. Vice-President: Once the president has been chosen, there are now only two remaining candidates for this position. Therefore, there are 2 possible choices for the vice-president.
3. Secretary: After the president and vice-president have been chosen, only one candidate remains for the secretary position. Hence, there is only 1 possible choice for the secretary.
To find the total number of ways to form the set of class officers, we multiply the number of choices for each position:
Total number of ways = Number of choices for president × Number of choices for vice-president × Number of choices for secretary
Total number of ways = 3 × 2 × 1 = 6
Therefore, the correct answer is c. 6.