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February 27th, 2016, 09:54 PM  #1 
Newbie Joined: Feb 2016 From: Mysore Posts: 2 Thanks: 0  Can you permute this
Here's a question"5 persons enter a lift cabin on the ground floor of an 8 floor house. Suppose each of them can leave a floor independantly at any floor begining from first floor.Find the total number of ways in which each of the 5 person can leave the cabin at any one of the 7 floors (need not be different floors)" As my answer i thoght there are 5 ways of leaving first , 5 for the second and third and 4th...and 7th so it should be 5^7 but the answer given is 7^ 5 ..Where am i wrong ?? 
February 28th, 2016, 12:24 AM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
The first person can leave on any of $7$ floors. The second person can leave on any of $7$ floors. etc. This gives $7^5$ possibilities. 
February 28th, 2016, 03:56 AM  #3 
Newbie Joined: Feb 2016 From: Mysore Posts: 2 Thanks: 0  
February 29th, 2016, 01:08 AM  #4 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244  You've said that there are 5 ways of leaving first. How do you figure? When the first passenger leaves, he may leave on either the 1st, 2nd, 3rd, 4th, 5th, 6th or 7th floors. Thus there are actually 7 ways of leaving first.


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