<p>In the integer 3589 the digits are all different and increase from left to right. How many integers between 4000 and 5000 have digits that are all different and that increase from left to right?</p>
<p>The answer is 10. Which ten solutions are they and is there any easy method to do this problem?</p>
<p>First digit clearly must be 4. The other three digits are all different and are a subset if {5, 6, 7, 8, 9}. Each subset of three digits uniquely determines a 4-digit number with increasing digits, so the number of such numbers is 5C3 = 10.</p>
<p>^I’ve always liked that solution to this problem – it’s very elegant.</p>
<p>But it is worth remembering that you don’t HAVE to use nCr on the SAT. An organized list will work:</p>
<p>4567, 4568, 4569, 4578, 4579, 4589, 4678, 4679, 4689, 4789</p>
<p>This would be a pain if there were lots more digits to worry about. But then it wouldn’t be an SAT problem anymore.</p>
<p>an easier way to do it if you don’t like dealing with combinations and permutations and remembering what’s what is to just make a quick list. You can easily go through all the combinations: 567, 568, 569, 578, 579, 589, 678, 679, 689, 789</p>