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?
It seems natural to set up recursion relations, as is common in enumerative combinatoric problems of this kind. Then to work with generating function methods.
Maybe based on something like this:
 G1(N) = # of ways for the last player to get his ball, given that the second player takes his own colour.
 G2(N) = # of ways for the last player to get his ball, given that the second player can't take his own colour.
 B1(N) = # of ways for the last player to fail to get his ball, given that the second player takes his own colour.
 B2(N) = # of ways for the last player to fail to get his ball, if the second player doesn't have his own colour available to him.
where N = # of balls at the start.

Posted by FrankM
on 20190501 05:11:48 