Lazy Larry's Random Algorithm

Probability Level 4

Lazy Larry was assigned to create a bubble sort algorithm, but he didn't have the time to do it properly. He designed the following algorithm instead:

For each iteration of the algorithm:


  • Choose two distinct elements in the list uniformly at random.

  • Exchange the placements of those elements in the list.

  • Check to see if the list is now sorted. If it is, end the algorithm. Otherwise, do another iteration.

Lazy Larry tests his algorithm on the following list:

capybara, dingo, aardvark, bandicoot

What is the expected value of the number of iterations of Larry's algorithm to alphabetize the list (A to Z)?


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