
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
October 19th, 2017, 07:52 PM  #1 
Newbie Joined: Oct 2017 From: United States Posts: 7 Thanks: 1  Counting Prin. & Binomial T.
So, I'm trying to focus heavily on mastering this topic for my upcoming meet. This is a 5point question, and I have yet to understand the process to get to the answer. Question: Find the number of positive integers less than 10,000 with all distinct digits. Any possible ideas? Also what are "distinct" digits exactly? Thanks! 
October 19th, 2017, 11:08 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out. 
I would assume the digits themselves aren't distinct, but they are distinct from other digits in a given number. 331  1 number, 3 digits, 2 distinct. Require 3 distinct. 123  all distinct Last edited by Joppy; October 19th, 2017 at 11:10 PM. 
October 20th, 2017, 02:07 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
Let's start counting: the onedigit whole numbers are 1 to 9, that's 9 numbers; the twodigit whole numbers are 10 to 98, excluding 11, 22, 33, 44, 55, 66, 77 and 88, so that's another 81 numbers; now you have a go at counting the threedigit and fourdigit whole numbers. Hint: consider what the digits can be if no two are the same for the same whole number. 
October 21st, 2017, 04:26 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
I don't know what Joppy means by "the digits themselves aren't distinct". The individual digits are "distinct" from what?

October 22nd, 2017, 06:44 AM  #5  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out.  Quote:
If we choose a single arbitrary number, is it distinct? Or can a distinction only be made when we have more than one number?  
October 22nd, 2017, 07:03 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond 
$$\{\varnothing\}$$

November 2nd, 2017, 07:12 PM  #7 
Newbie Joined: Oct 2017 From: United States Posts: 7 Thanks: 1 
Was able to figure it out eventually. Thanks for all the help guys!


Tags 
binomial, counting, prin 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
counting  shunya  Probability and Statistics  4  January 20th, 2016 06:58 AM 
How to resolve binomial experiment without binomial theorem.  beesee  Probability and Statistics  5  September 18th, 2015 01:38 PM 
counting  panky  Algebra  4  October 24th, 2012 10:02 AM 
More Counting  roguebyte  Advanced Statistics  4  February 3rd, 2012 06:41 PM 
More Counting  roguebyte  Applied Math  0  December 31st, 1969 04:00 PM 