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Math Help - Problem involving factorials and "choosing"

  1. #1
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    Problem involving factorials and "choosing"

    Q: Using the identity nC{r-1} + nCr = {n+1}Cr. Find a value of n which satisfies the equation:
    4C{n-1} + 4Cn = 5.

    My attempted solution:

    4C{n-1} + 4Cn = 5
    5Cn = 5 (by the identity given)
    {5!}/{n!(5-n)!}=5
    4! = n!(5-n)!

    Then i'm stuck - I can get the answer by trial and error using the fact that n is obviously between 0 and 4 and also by comparing with Pascal's triangle at the second line of work but I'm convinced that there must be a way by carrying on with the algebra.


    Thanks in advance for any help and apologies for not using LATEX i did try but failed badly.
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  2. #2
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    Quote Originally Posted by MrT83 View Post
    Q: Using the identity {^nC_{r-1}} + {^nC_r} = {^{n+1}C_r. Find a value of n which satisfies the equation:
    {^4C_{n-1}} + {^4C_n} = 5.

    My attempted solution:

    {^4C_{n-1}} + {^4C_n} = 5
    {^5C_n} = 5 (by the identity given)
    {5!}/{n!(5-n)!}=5
    4! = n!(5-n)!

    Then i'm stuck - I can get the answer by trial and error using the fact that n is obviously between 0 and 4 and also by comparing with Pascal's triangle at the second line of work but I'm convinced that there must be a way by carrying on with the algebra.


    Thanks in advance for any help and apologies for not using LATEX i did try but failed badly.
    I think that your method is as good as any. It involves a little bit of trial and error at the end, but I think that is unavoidable here.

    To see the LaTeX code, hover the cursor over the formulas. Each formula needs to be wrapped in [tex] [/tex] tags.
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  3. #3
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    Quote Originally Posted by Opalg View Post
    To see the LaTeX code, hover the cursor over the formulas. Each formula needs to be wrapped in [tex] [/tex] tags.
    Thanks! I think the problem was that I was wrapping with [tex]
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