A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathmath333

  • one year ago

How many 4 digit numbers are there whose decimal notation contains not more than 2 distinct digits ?

  • This Question is Closed
  1. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \(\large \color{black}{\begin{align} & \normalsize \text{ How many 4 digit numbers are there whose decimal notation}\hspace{.33em}\\~\\ & \normalsize \text{ contains not more than 2 distinct digits ? }\hspace{.33em}\\~\\ & a.)\ 672 \hspace{.33em}\\~\\ & b.)\ 576 \hspace{.33em}\\~\\ & c.)\ 360 \hspace{.33em}\\~\\ & d.)\ 448 \hspace{.33em}\\~\\ \end{align}}\)

  2. Drigobri
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    B) 576 is the answer

  3. MrNood
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how do we know you are right? a straight answer like this is no use to anyone please explain how you derived it, or better still give the poster the method , and let HIM derive it

  4. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Note to self: No silly mistakes. No silly mistakes. No silly mistakes.

  5. imqwerty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well what do u mean by decimal notation here :/ sry u posted one more question like decimal notation i got stuck there too

  6. imqwerty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sry to ask such a silly ques

  7. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    decimal notaion ={0, 1,2,3,4,5,6,7,8,9,} i think

  8. imqwerty
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    http://prntscr.com/8kc5b1 :/

  9. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    If there is only one unique digit then there are 9 such numbers (1111, 2222, ...) If there are two unique digits: First, consider all numbers where zero does not appear. (i) Three of one digit and one of the other one. \(9\cdot \binom{4}{3} \cdot 8\) (ii) Two of each digit \(9\cdot \binom{4}{2}\cdot 8\) Now consider those numbers where zero does appear. (i) Three zeroes and one other digit. This can only be done in 9 ways (1000, 2000, ...) (ii) Two zeroes and two of the other digit. This can be done in \(9\cdot \binom{3}{2}\)

  10. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I think "decimal notation" means nothing but base 10 integers here.

  11. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    (iii) One zero and three of other digits.\[3\cdot 9~ways \]

  12. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    wow why am I getting 765

  13. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    @ganeshie8 !!!

  14. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Can you spot any mistake?

  15. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think u double counted something

  16. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    What?

  17. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I'm actually getting 765 + 27 = 792 :P

  18. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Slightly modified : If there is only one unique digit then there are 9 such numbers (1111, 2222, ...) If there are two unique digits: First, consider all numbers where zero does not appear. (i) Three of one digit and one of the other one. \(9\cdot \binom{4}{3} \cdot 8\) (ii) Two of each digit \(9\cdot \dfrac{\binom{4}{2}}{\color{red}{2}}\cdot 8\) Now consider those numbers where zero does appear. (i) Three zeroes and one other digit. This can only be done in 9 ways (1000, 2000, ...) (ii) Two zeroes and two of the other digit. This can be done in \(9\cdot \binom{3}{2}\) (iii) One zero and three of the other digit. This can be done in \(\color{red}{9\cdot \binom{3}{1}}\) @ParthKohli

  19. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    why would you change \(\binom{3}2\) to \(\binom{3}1\) and good catch

  20. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.