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A committee is to be made up from a group of 10 candidates. The committee must consist of a chairman and some (not necessarily nonzero) number of members-at-large. How many ways can the committee be chosen? (For example, suppose that Alex is chair while Betty, Carl, and D'Angelo make up the committee. This counts as the same as Alex being chair while Carl, Betty, and D'Angelo make up the committee. It is not the same as Betty being the chair, with Alex, Carl, and D'Angelo making up the committee. It is also not the same as Alex being chair with the committee consisting of Betty and Carl.)

tertre  Feb 16, 2018

Best Answer 

 #1
avatar+93367 
+3

A committee is to be made up from a group of 10 candidates. The committee must consist of a chairman and some (not necessarily nonzero) number of members-at-large. How many ways can the committee be chosen?

 

Chairman+0        10                                       =    10 ways

Chairman+1        10*9                                    =   90 ways

Chairman+2        10*9C2       = 10*36            =   360 ways         

Chairman+3         10*9C3      =  10*84           =   840 ways        

Chairman+4         10*9C4      =    10*126       =   1260 ways        

Chairman+5         10*9C5      =    10*126       =   1260 ways  

Chairman+6          10*9C6      =  10*84           =   840 ways

Chairman+7         10*9C7       = 10*36            =   360 ways

Chairman+8        10*9C8        = 10*9            =   90 ways       

Chairman+9        10                                      =    10 ways         

 

Now you can add up all the ways  :)       

Melody  Feb 17, 2018
 #1
avatar+93367 
+3
Best Answer

A committee is to be made up from a group of 10 candidates. The committee must consist of a chairman and some (not necessarily nonzero) number of members-at-large. How many ways can the committee be chosen?

 

Chairman+0        10                                       =    10 ways

Chairman+1        10*9                                    =   90 ways

Chairman+2        10*9C2       = 10*36            =   360 ways         

Chairman+3         10*9C3      =  10*84           =   840 ways        

Chairman+4         10*9C4      =    10*126       =   1260 ways        

Chairman+5         10*9C5      =    10*126       =   1260 ways  

Chairman+6          10*9C6      =  10*84           =   840 ways

Chairman+7         10*9C7       = 10*36            =   360 ways

Chairman+8        10*9C8        = 10*9            =   90 ways       

Chairman+9        10                                      =    10 ways         

 

Now you can add up all the ways  :)       

Melody  Feb 17, 2018
 #2
avatar+3048 
+1

Amazing, Melody! Great job!

tertre  Feb 17, 2018

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