SOLUTION: Club members are going to elect their officers. If there are four candidates for
president, 3 for vice president, and 2 for secretary, then how many ways can the
officers be el
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-> SOLUTION: Club members are going to elect their officers. If there are four candidates for
president, 3 for vice president, and 2 for secretary, then how many ways can the
officers be el
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Question 1193984: Club members are going to elect their officers. If there are four candidates for
president, 3 for vice president, and 2 for secretary, then how many ways can the
officers be elected? Found 2 solutions by math_tutor2020, ikleyn:Answer by math_tutor2020(3817) (Show Source):
Why does this work?
Well let's consider just the president and VP for now.
We have 4 people for president and 3 for VP.
Make a table with 4 rows and 3 columns.
The rows correspond to the candidates for president, while the columns are for VP.
This table has 4*3 = 12 inner cells to show the twelve different president/VP combos.
To further extend this thought exercise, now consider a table with 12 rows and 2 columns.
The rows represent all the possible president/VP combos covered in the previous paragraph.
The columns represent the different possibilities for secretary.
This second table has 12*2 = 24 different cells. Each of the 24 cells shows a different combo of president/VP/secretary.
We can rewrite 12*2 = 24 into 4*3*2 = 24 to see why we multiply the values.
Side note: Optionally you could create a tree diagram to help see all the possible outcomes.
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