<p>How many numbers greater than 200 but less than 10,000 can be formed from 0,1,2,3,4 assuming digits may be repeated?
a)501
b)549
c)550
d)574
e)575</p>
<p>The answer key says E, but I'm getting D. Is the key wrong or am I wrong? Thanks.</p>
<p>3 digit numbers (201-444):
1st digit can be anything but 0 or 1
other 2 digits can be anything, so: 3x5x5
But that set will include 200, which you don't want, so 3x5x5 - 1</p>
<p>4 digit numbers (1000-4444):
1st digit can be anything but 0
other digits can be anything, so: 4x5x5x5</p>
<p>74 + 500 = 574. So that means I'm getting the same thing you are... I'm not the greatest at that type of problem, but I'm pretty sure what I did was right...</p>
<p>I also got 574.</p>
<p>If we count ALL numbers < 10,000, we have</p>
<p>0 _ _ _ _</p>
<p>which gives</p>
<p>1 * 5^4 = 625 numbers</p>
<p>However, there are 50 numbers < 200:</p>
<p>0 0 (0,1) _ _</p>
<p>2 * 5^2 = 50 numbers</p>
<p>Which brings us down to 575. However, since we are ALSO counting out 200, we must reduce the final answer to 574.</p>
<p>Are you sure that the exact wording is "greater than 200 but less than 10,000"? If so, then I'd say that whoever calculated the answer in the book is plotting to lower your score.</p>
<p>Every book has typos; ya gotta expect that.</p>
<p>thecomisar, I'm going nuts waiting for my subject test scores so you must forgive an odd theory or two. (D ane E ard fairly closd on thd kdyboare so you'rd probably right.)</p>
<p>haha... gooe luck on your scords :)</p>