
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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April 27th, 2018, 01:48 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  Why did we subtract 1 from 5?
If 4 persons are invited for a party, find the number of ways in which they can be seated around a table along with the host. Solution: Including the host, we have five persons. Now, 5 persons can arrange themselves around a table in (51)! = 4! = 24 ways. 
April 27th, 2018, 05:09 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
Because they are only counting the relative positions. Everybody shifting one or two places to the left, for example, would be counted as the same order.

April 27th, 2018, 10:17 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
April 27th, 2018, 11:31 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,281 Thanks: 1965  Seating.PNG The arrangements above have different positions for H (the host) but would be counted as the same if the seating order is all that matters. 

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