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February 27th, 2016, 08:54 PM   #1
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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 ??
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February 27th, 2016, 11:24 PM   #2
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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.
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February 28th, 2016, 02:56 AM   #3
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Quote:
Originally Posted by Azzajazz View Post
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.
I agree but what is wrong in my approach.
Any one of 5 people can get down at flr1 same for flr2 and so on. so 5^7
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February 29th, 2016, 12:08 AM   #4
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Quote:
Originally Posted by iamashwin99 View Post
As my answer i thoght there are 5 ways of leaving first , 5 for the second and third and 4th...and 7th
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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