My Math Forum Doubt in Counting

 Probability and Statistics Basic Probability and Statistics Math Forum

 December 10th, 2016, 02:24 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, 06:54 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 881 Thanks: 353 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, 08:11 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, 08:47 PM   #4
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 Originally Posted by Prudhvi raj k 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 ?
If you are insisting that the digit chosen for example in the 10's place not be one of the digits chosen in the 1000's or 100's place, then of course that selection is not independent of the previous selections.

 December 14th, 2016, 09:57 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, 10:10 PM   #6
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 Originally Posted by Prudhvi raj k 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 ?
The events are not independent. What you really end up with is a product string of conditional probabilities.

Jeff1 has given you the correct answer and reasoning in post #2.

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