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April 27th, 2018, 02:22 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 295 Thanks: 1  How to understand this solution?
In how many ways can a team of four be selected from eight players? 1) When one player is always included? 2) When one player is always excluded? Solution: 1) Since one player is always included, then we have to select three players from seven which can be done in 7C3 ways. 2) Since one player is always excluded then we have to select 4 players from 7 which can be done in 7C4 ways. My question: why in both cases 7 is taken instead of 8? I mean 7C3 and 7C4 etc. 
April 27th, 2018, 04:07 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
In the first problem "one player is always included" so we select the remaining 3 players from the other 7. In the second problem "one play is always excluded" so we can ignore him and choose all four players from the other 7. Last edited by skipjack; April 27th, 2018 at 06:44 AM. 
April 27th, 2018, 06:47 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,291 Thanks: 1683 
The question is unclear anyway, as "team" isn't defined.


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