
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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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: 1,801 Thanks: 636 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: 20,640 Thanks: 2083 
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: 1,801 Thanks: 636 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: 7,935 Thanks: 1129 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!


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binomial, counting, prin 
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