Question 1173260
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<pre>

"Less than 2,000"  means that the first digit is  " 1 "  (thousand's digit).


So, first digit is fixed;  it is the digit  " 1 ".


In the rest 3 positions, any of 8 digits from 2 to 9 can be.


It gives  8*8*8 = {{{8^3}}} = 512 opportunities and 512 possible 4-digit numbers,
under given condition.
</pre>

Solved.


This solution is produced assuming that repeating is allowed.


If repeating is not allowed, then the answer is 8*7*6 = 336.


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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Simple and simplest problems on permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Special-type-permutations-problems.lesson>Special type permutations problems</A> 

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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>

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