Ms. G has 8 boys and 6 girls in her class. The class is going to elect a president, vice president, secretary, and treasurer. Tom and Ruth, members of the class are no longer speaking and will not work together. If all members of the class are willing to be considered for any of the offices and any slate of officers with tom and ruth is an unworkable slate, how many workable slates of officers could be considered?
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Ms. G has 8 boys and 6 girls in her class.
The class is going to elect a President, Vice President, Secretary, and Treasurer.
Tom and Ruth, members of the class are no longer speaking and will not work together.
If all members of the class are willing to be considered for any of the offices
and any slate of officers with Tom and Ruth is an unworkable slate,
how many workable slates of officers could be considered?
There are: . possible outcomes.
Suppose Tom and Ruth are elected.
Tom can have any of the 4 positions.
Ruth can have any of the other 3 positions.
The other two positions are filled by two of the other 12 students.
. . There are: . ways.
Hence, there are: . unworkable slates.
Therefore, there are: . workable slates.