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


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October 19th, 2017, 08:52 PM   #1
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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!
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October 20th, 2017, 12:08 AM   #2
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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 20th, 2017 at 12:10 AM.
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October 20th, 2017, 03:07 AM   #3
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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.
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October 21st, 2017, 05:26 AM   #4
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I don't know what Joppy means by "the digits themselves aren't distinct". The individual digits are "distinct" from what?
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October 22nd, 2017, 07:44 AM   #5
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Quote:
Originally Posted by Country Boy View Post
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?
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October 22nd, 2017, 08:03 AM   #6
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November 2nd, 2017, 08:12 PM   #7
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Was able to figure it out eventually. Thanks for all the help guys!
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