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Combination question

  1. Sep 23, 2011 #1
    How many sequences of zeros and ones of length 7 contain exactly 4 ones and 3 zeros?

    I'm having a hard time figuring out why it is 7 Chooses 4?

    thx
     
  2. jcsd
  3. Sep 23, 2011 #2
    Select any four spaces within the seven spaces in 7C4 ways, and put 1's in each of the four spaces. Where can all the zeros go now? Notice the identity 7C4=7C(7-4)=7C3. Can
    you see, in the context of this problem , why 7C4=7C3?
     
  4. Sep 24, 2011 #3
    Yes, because we for 3 zeros and 4 ones.
     
  5. Sep 24, 2011 #4
    Exactly. Perfect. This is the general identity nCk =nC(n-k).
     
  6. Sep 25, 2011 #5
    Thank you :)
     
  7. Sep 28, 2011 #6
    No problem; glad to help.
     
  8. Sep 29, 2011 #7

    chiro

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    Science Advisor

    If you want to get some intuition, what you can do is to start with 1111000, and then find every way of re-arranging these digits so that each rearrangement is different from each other. For example 1111000 goes to 1110100, 1110010, 1110001 and so on.

    Using this as your intuition base, you can develop a factorial relationship which will eventually give you the "N choose R" formula that you use.
     
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