<p>Hello,</p>
<p>The following is a problem that has me completely stumped:</p>
<hr>
<p>How many different 4-digit integers can be created, by using only the digits 2, 4, 5, 6, and 8, provided that all of the 4-digit integers are greater than 5,000, and that any digit CAN be repeated?</p>
<hr>
<p>The correct formulas needed to solve this problem escape me. Instead, the only way I can figure out how to solve this problem is to make a long hand-written list and count the total number of 4-digit numbers, given the criteria cited above.</p>
<p>Any assistance on this problem would be deeply appreciated.</p>
<p>Thanks in advance.</p>
<p>Dennis</p>
<p>Think about selecting the digits starting with the leftmost … the one in the thousandths slot. There are 3 possible choices for this digit (since the number is >5000) – i.e. 5, 6. and 8.</p>
<p>Now move to the hundredths digit. There are 5 possible choices – 2, 4, 5, 6, and 8.</p>
<p>And for the tenths digit. Again 5 possible choices – 2, 4, 5, 6 and 8.</p>
<p>And for the ones digit. Again the same 5.</p>
<p>Total number of distinct choices is the product: 3<em>5</em>5*5 = 375</p>
<p>If you’ve not done problems like this before, try a simpler version: how many even 2 digit numbers greater than 50 can you create from 5, 2, and 1.</p>
<p>Hello Fogcity,</p>
<p>Thank you very much for your solution and explanation for this problem.</p>
<p>It all makes sense now.</p>
<p>What was confusing me the most was the stipulation that any digit could be repeated.</p>
<p>Thanks again!</p>
<p>Dennis</p>