A postman has to deliver 4 letters to a 4 places, he delivers all of them to the wrong places. What is the number of cases in which it is true?

Question

anonymous · Answer

suppose A,B,C,D represent the letters mailed in the correct order to the 4 people.
How many ways can we send letters so that each one receives the wrong letter
B,C,D,A
C,D,A,B
D,A,B,C
B,A,D,C
D,C,B,A...

wolf1728 · Answer

In which what is true? You mean in how many ways can he deliver 4 letters to the wrong 4 places? This has to do with a math concept known as "derangements". We could figure this by trial and error. We have four letters which ALL must get delivered to the incorrect address. So let's say letter 1 cannot go to address 1, letter 2 cannot go to address 2 and so on. Basically, we have to determine how many ways we can arrange the numbers 1 2 3 and 4 WITHOUT 1 in place 1, 2 is NOT in place 2, etc. There are NINE such combinations: 2143 2341 2413 3142 3412 3421 4123 4312 4321 Is there a formula? Yes. Number of derangements = n! * (1-1/1! +1/2! -1/3! + 1/4!) Number of derangements = 4! * (1 -1 + (1/2) -(1/6) + (1/24) Number of derangements = 24 * (0 +(1/2) -(1/6) + (1/24) Lowest common denominator of the fractions = 24 Number of derangements = 24 * (0 +(12/24) -(4/24) + (1/24) Number of derangements = 24 * (9/24) Number of derangements = 9 For a calculator and more explanation go here: http://www.1728.org/derange.htm

wolf1728 · Answer

LOL jayzdd gets the medal for an INCORRECT answer ??? !!!
The answer is NINE!!
LOL

wolf1728 · Answer

Heck, I'LL send a medal to jayzdd too!!!

anonymous · Answer

I did not finish

wolf1728 · Answer

Well that is okay.  I was not really assigning any blame to you - just those medal awarders.
(And why are medals awarded BEFORE someone finishes?)

anonymous · Answer

Using  numbers, assuming 1,2,3,4 is the correct order. 
I get the same

2,1,4,3
2,3,4,1
2,4,1,3
3,1,4,2
3,4,1,2
3,4,2,1
4,1,2,3
4,3,1,2
4,3,2,1

anonymous · Answer

Nice derangement formula. I did this by making a tree which is tedious

wolf1728 · Answer

Hello to ganeshie8 :-)

wolf1728 · Answer

Or you could have just copied my numbers :-)

anonymous · Answer

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