My Math Forum Counting Prin. & Binomial T.

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 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 5-point 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 one-digit whole numbers are 1 to 9, that's 9 numbers; the two-digit 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 three-digit and four-digit 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:
 Originally Posted by Country Boy I don't know what Joppy means by "the digits themselves aren't distinct". The individual digits are "distinct" from what?
It's possible that I don't either! For some 'thing' to be distinct, it must be compared with other 'things' of that type (?).
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 $$\{\varnothing\}$$ Thanks from Joppy
 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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