Six balls are at the front of the classroom, and six students are each assigned a different colored ball.

Then they are asked to go up one at a time and take the ball they were assigned.

However, the first student doesn't like the color he was assigned, so he picks randomly from the remaining five.

After that, each successive student takes the color they were assigned if it's available, otherwise they choose randomly from the remaining balls.

What is the probability that the last student gets the ball they were assigned?

(In reply to re: computer assissted solution by Steven Lord)

Thank you for pointing this out.  I had tried an analytic approach and was writing my thoughts as I went along. But then I gave up that approach and wrote a string of x's.  I forgot to start the copying for pasting into the comment here, at those x's.  I've gone back now and deleted everything before the program listing.

Posted by Charlie on 2019-04-25 15:30:08