Brain Teasers
Problems With the Windy City
Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability
In how many different ways can you rearrange the letters in the word "CHICAGO"?
Hint
There are two C's in "CHICAGO".Answer
At first glance, the response may seem to be simply 7!, or 5040. However, duplicates of the letter "C" poses a problem in the response. Any combination of letters, such as "ICCHOGA" can be created with C#1 coming first followed by C#2 or with C#2 preceding C#1. Any distinct possibility comes in pairs such as this. Therefore, to get rid of all duplicates, we divide 5040 (7!) in half to arrive at 2520, the answer to this problem.Hide Hint Show Hint Hide Answer Show Answer
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Comments
Now this is my street. I got it right! Yay! Great teaser despie its easiness in my eyes
Good Teaser, took me awhile to figure it out though.
Blown. A. Way. no, really it was pritty good
Help me out here: Why would it not be 6x6x5x4x3x2x1? Thanks.
feeling dumb.
feeling dumb.
I agree with Riddlerman
dude, i was really blown away by that. by before i got plum loco, i got it.
Good one that was pretty hard. I knew what to do just didnt know i had to divide by by 2 or wat.
i feel blonde..............and my hair is black
I agree with turtles..
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What ???????????????????????????
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HUH!
OMG, I got a tough one! It would have been a lot easier if Chicago started with an "S", the way it sounds.
Well the question says how many ways can you REARRANGE the letters so it would be 2519 ways.
Once in a while I come to this site and actually get a teaser right Thanks
I agree with Jimbo: you need to subtract the original arrangement of the letters.
You can generalize the solution of the ways to arrange N items with repeated elements as
N!/(A!*B!*C!...)
where A, B, C, etc. are the counts of each distinct element. Thus the number of ways to arrange the letters in MISSISSIPPI is
11!/(4!*4!*2!)
= 39916800/(24*24*2)
= 34650
and the number of ways to rearrange the letters is 34650 - 1.
You can generalize the solution of the ways to arrange N items with repeated elements as
N!/(A!*B!*C!...)
where A, B, C, etc. are the counts of each distinct element. Thus the number of ways to arrange the letters in MISSISSIPPI is
11!/(4!*4!*2!)
= 39916800/(24*24*2)
= 34650
and the number of ways to rearrange the letters is 34650 - 1.
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