Results 1 to 7 of 7

Math Help - letter in envelope problem

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    3

    letter in envelope problem

    i not getting the correct answer for this sum : In how many ways can five letters be placed in five envelopes such that exactly one letter goes into corresponding envelope?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,712
    Thanks
    1642
    Awards
    1
    Quote Originally Posted by dukes123 View Post
    i not getting the correct answer for this sum : In how many ways can five letters be placed in five envelopes such that exactly one letter goes into corresponding envelope?
    It is hard to know exactly what you are asking.

    But this may be it.
    A derangement is rearrangement of a collection in which no element remains fixed.
    So you can chose one of five to be fixed and then derange the other four.
    So, 5\cdot D(4)=5(9)=45.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,792
    Thanks
    1532
    Quote Originally Posted by dukes123 View Post
    i not getting the correct answer for this sum : In how many ways can five letters be placed in five envelopes such that exactly one letter goes into corresponding envelope?
    Do you mean exactly one letter goes into each envelope?

    You have 5 choices which letter to put into the first envelope, then 4 choices which to put in the second envelope, then 3, then 2, then 1. 5*4*3*2*1= 5!

    This is exactly the same as the number of different ways to order 5 objects.

    Plato's answer was assuming that each letter had a correct envelope and you were asking "how many ways can you put 5 letters in 5 evelopes if no letter goes into the correct envelope". I did not interpret your question that way.
    Last edited by HallsofIvy; November 7th 2009 at 03:30 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2009
    Posts
    3
    hey plato your answer is correct
    plz explain how u got D(4)=9 its little confusing for me
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,712
    Thanks
    1642
    Awards
    1
    Quote Originally Posted by dukes123 View Post
    hey plato your answer is correct
    plz explain how u got D(4)=9 its little confusing for me
    Here is a very helpful website for derangements

    Here is a formula: D(n) = n!\sum\limits_{k = 0}^n {\frac{{( - 1)^k }}{{k!}}} .

    Here is a good approximation: n \geqslant 4\, \Rightarrow \,D(n) \approx \frac{n!}{e}.

    D(4)=\frac{4!}{e}\approx 8.8291, so D(4)=9
    Last edited by Plato; November 6th 2009 at 10:08 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2009
    Posts
    3
    thks a lot !! got to learn somethin new today
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,792
    Thanks
    1532
    Oh, I see now. "exactly one letter goes into corresponding envelope" means exactly one letter goes into the correct envelope and the other four into the wrong envelopes.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: November 30th 2010, 03:31 AM
  2. Helix, arc tangent envelope
    Posted in the Geometry Forum
    Replies: 0
    Last Post: November 9th 2010, 08:01 PM
  3. Envelope and letter problem ?
    Posted in the Statistics Forum
    Replies: 2
    Last Post: March 29th 2009, 10:21 PM
  4. Envelope Of st
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 16th 2008, 11:33 PM
  5. [SOLVED] [SOLVED] Letter and number substitution problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 7th 2008, 04:07 PM

Search Tags


/mathhelpforum @mathhelpforum