A community for students.
Here's the question you clicked on:
 0 viewing
sh3lsh
 one year ago
How many positive integers less than 1000 have distinct digits?
Is there a way to approach through combinatorics?
sh3lsh
 one year ago
How many positive integers less than 1000 have distinct digits? Is there a way to approach through combinatorics?

This Question is Closed

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0i would say they all have distinct values !

sh3lsh
 one year ago
Best ResponseYou've already chosen the best response.0Oh, I'm sorry. Have distinct digits!

misty1212
 one year ago
Best ResponseYou've already chosen the best response.010 choices for the first digit, then 9 for the second and finally 8 for the third counting principle from there

sepeario
 one year ago
Best ResponseYou've already chosen the best response.0damn this could be hard..

sepeario
 one year ago
Best ResponseYou've already chosen the best response.01digit integers: 1, ..., 9  there are 9 integers. 2digit integers: 10, ..., 99  there are 90 integers, but in 9 of them (11, ..., 99) the two digits are the same. So there are 90 − 9 = 81 2digit integers with distinct digits. Another way to get this answer is to consider the number of possibilities for each digit: the first digit can be any nonzero digit, so it has 9 choices. The second digit can be any digit except equal to the first one, so it has 9 choices too. There are 9 · 9 = 81 choices total. 3digit integers: 100, ..., 999  there are 900 integers total, but some of them have a repeating digit... The number of 3digit integers with distinct digits can be counted as follows: the first digit can be any nonzero digit, so it has 9 choices. The second digit can be any digit except equal to the first one, so it has 9 choices too. Finally, the third digit can be any digit except equal to the first digit or the second digit, so it has 8 choices. There are 9 · 9 · 8 = 648 choices total. So there are 9 + 81 + 648 = 738 positive integers less than 1000 wit distinct digits.

sepeario
 one year ago
Best ResponseYou've already chosen the best response.0http://mail.csufresno.edu/~mnogin/math114fall04/4118sol.pdf

sepeario
 one year ago
Best ResponseYou've already chosen the best response.0or you could just read that ^ :)

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.2You can use some combinatorics, but really just a little multiplication. 1000 does not have unique digits. It's out Let's look at the rest  0  999 * 19 : 9 total, all distinct * 1099 : 9*9=81 distinct, because 11,22,33,44,55,66,77,88,99 are removed (that is 909=81 distinct numbers). Note, in the MSD, 19 are allowed, in the second digit, 09 are allow, but we need to take out the digit that was used in MSD, leaving 9 digits for the LSD * 100999: 9*9*8=648 distinct, for similar reasons Total = 9+81+648 = 738 distinct numbers

sh3lsh
 one year ago
Best ResponseYou've already chosen the best response.0Thanks a bunch you all!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.