You are given 10 cell phones and 10 cell numbers(each number corresponds to one of each of those 10 cell phones), but you don't know which number corresponds to which cell phone. Your task is to label each cell phone with its corresponding number. Using optimal procedures, what is the probability that you will finish the task in exactly 5 attempts?

A single attempt is defined as calling a number from a cell phone.

Hint: The caller's number will be displayed in the cell that is being called.

(In reply to re(3): Solution? by Jyqm)

Indeed, the system will tolerate one self-call regardless of where in the sequence it occurs. We considered the last one to be a possibility as well as the possibility that no self-calls were made. We need also consider the other four possibilities, which are all mutually exclusive, so we can add the probabilities:

9/10*7/8*5/6*3/4
+ 1/10*8/9*6/7*4/5*2/3
+ 9/10*1/8*6/7*4/5*2/3
+ 9/10*7/8*1/6*4/5*2/3
+ 9/10*7/8*5/6*1/4*2/3

= 153947/201600

~= 0.7636259920634920634

Posted by Charlie on 2008-06-11 19:53:25