Julia such a passcode and her tablet which only allows five digit codes she has heard that it's more secure if I digit is repeated in the passcode what is the probability the spies is able to unlock the tablet on his first try

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Julia such a passcode and her tablet which only allows five digit codes she has heard that it's more secure if I digit is repeated in the passcode what is the probability the spies is able to unlock the tablet on his first try

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Given that the password is 5 digit long and there is one digit repeating.The spy knows 4 digits.He can pick the repeating digit from 4 digits in 4 ways.When the repeating digit is picked, then other 3 digits can be picked from other (4-1)=3 digits in 3C3=1 wayWhen all the digits are picked then we can arrange them in 5!2!=60 waysSo total number of possible passwords=4×1×60=240 

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