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A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, not including Mark?

 Oct 28, 2024
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A baking club wants to form an executive committee. There are $15$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people, not including Mark?   

 

That depends.  If the two members have different ranks or titles, then there are 14P2  =  182 ways.    

This way would mean that a pair of members like Jesse and Frank is different from Frank and Jesse.    

 

If the two members are untitled and otherwise indistinguishable, then there are 14C2  =  91 ways.    

This way would mean that a pair of members like Jesse and Frank is the same as Frank and Jesse.  

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 Oct 28, 2024

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