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December 10th, 2016, 01:24 AM  #1 
Newbie Joined: Mar 2016 From: India Posts: 14 Thanks: 0  Doubt in Counting
How many numbers in the range 1000 9999 do not have any repeated digit? In solution how many ways that we can select a digit at 1's place and 10's place , 100's and 1000's .then we multiply them Consider selecting each digit at particular place is an event so My question is Are those events are independent or mutually exclusive ? because in solution we use product rule but those are looking like mutually exclusive events for mutually exclusive we use sum rule right ? Can you please help me out. Thank You in advance 
December 10th, 2016, 05:54 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,038 Thanks: 423 
There are 9 distinct ways to select the thousands digit (zero must be excluded). There are thus 9 remaining distinct ways to select the hundreds digit. There are 8 distinct ways to select the tens digit, and 7 distinct ways to select the units digit. So the answer is $9^2 * 8 * 7 = 4536.$ 
December 14th, 2016, 07:11 PM  #3 
Newbie Joined: Mar 2016 From: India Posts: 14 Thanks: 0 
Thank you sir but my doubt is In counting or probability : when any events are independent then we use product rule . Is Converse of this statement is also true ? for e.g : in above solution we have used product rule that's why we multiplied number of ways that we can select at each digit place. Is it mean that those are independent events ? 
December 14th, 2016, 07:47 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 1,980 Thanks: 1027  Quote:
 
December 14th, 2016, 08:57 PM  #5 
Newbie Joined: Mar 2016 From: India Posts: 14 Thanks: 0 
Yes sir am insisting that condition: then those are not independent events that means dependent events Again question is:Shall we use product rule in solving this dependent events ? I thought only in case of independent events we use product rule ?. Please make my understand clear in the relation of product rule and independent events ? 
December 14th, 2016, 09:10 PM  #6  
Senior Member Joined: Sep 2015 From: USA Posts: 1,980 Thanks: 1027  Quote:
Jeff1 has given you the correct answer and reasoning in post #2.  

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