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: Solution? by Fernando)

On the fifth try it doesn't matter if you've called the same phone; you've still identified the two phones that remain. So long as the first four tries were each to a phone other than itself, you've got it on the fifth call.

So don't multiply by that last 1/2.

The answer is thus 9/10*7/8*5/6*3/4 = 63/128 = .4921875.

Posted by Charlie on 2008-06-11 18:17:40