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If you randomly threw the 26 letters of the alphabet into the air, how many times would you need to throw them before they landed in order A-Z?

And if you allowed 1 1/2 seconds between each throw, how many years would it take?  I understand there is a lot of varibles in this question.  thanks

It's just an approximate

 Jan 24, 2025
 #1
avatar+28 
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since it could land in a-z order first try it could take only 1 1/2 seconds but if it was on the very last try it would (26^26)x1.5/amount of seconds in a year. 

 Jan 24, 2025
 #2
avatar+909 
+1

This is a fun thought experiment! Here's a breakdown of the calculations involved:

 

1. Number of Possible Arrangements

 

The number of ways to arrange 26 letters is given by the factorial of 26 (written as 26!).

 

26! is a huge number: approximately 4.03 x 10^26

 

2. Probability of Success

 

Assuming each arrangement is equally likely, the probability of getting A-Z in a single throw is 1 / 26!

 

3. Expected Number of Throws

 

The expected number of throws to achieve a specific outcome in a series of independent trials is 1 / probability of success.

 

Therefore, the expected number of throws to get A-Z is 26!

 

4. Time Calculation

 

Time per throw: 1.5 seconds

 

Total time: Expected number of throws * Time per throw

 

Total time in years: Total time in seconds / (60 seconds/minute * 60 minutes/hour * 24 hours/day * 365 days/year)

 

5. Result

 

The expected time to get A-Z is incredibly long.

 

It would take on the order of 10^26 years.

 Jan 25, 2025

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