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A Senate committee has 8 Republicans and 6 Democrats. In how many ways can we form a subcommittee of 5 members that has at least one member from each party?

 Mar 25, 2019
 #1
avatar+233 
+1

Seeing how we have low numbers, it's just trial and error. RRRRD, RRRDD, RRDDD, RDDDD, where R is Republicans and D is Democrats. It doesn't matter whether you do RRDRR or RRRRD, they are the same thing. So counting them, we have 4 possible scenarios. 

 

Hope this helps!

 Mar 25, 2019
 #2
avatar+99441 
+2

Total possible subcommittees =  C(14,5)   

Total possible subcommittees  that contain no Repubs = C(6,5)   [choose any 5 Dems from 6 ]

Total possible subcommittees that contain no Dems = C(8,5)   [ choose any 5 Repubs from 8 ]

 

So...the total number of subcommittees that contain at least one member of either party =

 

C (14,5) - C(6,5)  - C(8,5)   =   1940

 

 

cool cool cool

 Mar 25, 2019
edited by CPhill  Mar 25, 2019
edited by CPhill  Mar 25, 2019
 #3
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Sorry LagTho, but I believe Chpill is right

Guest Mar 25, 2019
 #4
avatar+233 
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That's fine. Sorry I couldn't be any help!

LagTho  Mar 25, 2019

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