+4 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
+28 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.
+909 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.
