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Number of unique paths in Pascal's Triangle

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Let pascal(n,i) be the value of the ith element of the nth row of Pascal's triangle. Using induction show that the number of unique paths from entry {0,0} to entry {n,i} in Pascal's triangle is equal to pascal(n,i).

    3. The attempt at a solution
    The base case n=1 seems easy enough to prove. It is obvious that there is only one path to each of the two elements in the nth row.

    It was brought to my attention that each value at {n,i} in Pascal's triangle can be represented by nCi.

    That being said I am not sure how to precede. I am just looking for some insight on how to continue.

    Any suggestions would be greatly appreciated.
     
  2. jcsd
  3. Feb 20, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Hint: How (from which elements) can you reach the ith element in the nth row, if movement is restricted in the appropriate way?
     
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