<p>How many four digit numbers do NOT have a units digit of 5?</p>
<p>Well.....simple question, complicated thought process.</p>
<p>I couldn't figure it out, can you?</p>
<p>assuming 1000-9999 are 4 digit numbers = 9,000</p>
<p>9,000 = 9 choices for thousands digit x 10 choices for hundreds digit x 10 for tens x 10 for ones
so if there are no fives, it’d be 8 choices for thousands x 9 choices for hundreds x 9 x 9 = 5832 numbers</p>
<p>another way to think of it:
starting with 9,000 numbers
minus 5000-5999 = 8,000
minus 1500-1599 which is 100 x 8 sets = 7,200
minus 1050-1059 which is 10 x 9 in each thousand x 8 sets = 6,480
minus 1005 which is 1 x 9 in each hundred x 9 in each thousand x 8 sets = 5,832</p>
<p>Isn’t it 8100? </p>
<p>I thought of it logically. There are 9000 numbers between 1000 and 9999. Having a 5 in the units place is once every ten numbers -> 10 every hundred -> 100 every thousand -> since there are 9 thousands, there are 900 numbers with 5 in the ones place. 9000-900=8100</p>
<p>Another way,
You have 9(thousands) * 10(hundreds) * 10(tens) * 9(ones)= 8100</p>
<p>Each number represents how many digits you can have in that spot.</p>
<p>I literally typed everything out fully explaining myself and my wifi decided to bail on me. I got 8100. I’ll retype my logic in an extremely summarized format. </p>
<p>There are a possible of 10 ones places, 10 tens places, and 9 thousands places. So, 10x10x9=900. 900 is the total amount of 4 number digits with a 5 in the ones (units) place. Now to find the amount of numbers that don’t have a 5 in the ones place, you find the total number of 4 digit numbers (9000) minus the amount of numbers that do have a 5 (900) and so you get 8100. 9000-900=8100.</p>
<p>It’s just 9<em>10</em>10*9. 9 options for the thousands place (any number except for 0), 10 options for hundreds place, 10 again for hundreds place and 9 for units digit( anything from 0-9 except 5).</p>
<p>It’s damn easy…for the thousands place take 8 digits(since 0 cannot be considered) and 9 digits for the the other three place(since 5 is discarded).
Then, 8<em>9</em>9*9=5,832</p>
<p>The answer is 8100. Thanks for the explanations, hope those who got it wrong can learn form their mistakes!</p>
<p>I can’t figure out why the total number of four digit numbers is 9000, anyone care to explain?</p>
<p>The first number (thousands place) has to be anything from 1-9, so it has 9 options (cant be 0 because a four digit number obviously can’t start with a 0). Second digit (hundreds place) can be 0-9, so it has 10 options. Same for the third and fourth digits. So the total number of possibilities is simply 9<em>10</em>10*10=9000.</p>
<p>^Logically, the highest 4 digit number is 9999 and the lowest is 1000. The total numbers between the two is 9000 (remember it’s inclusive).</p>
<p>^Agree, you do (9999-1000)+1 since 9999 and 1000 are both 4 digit numbers as well.</p>