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Possible Combinations

  1. Apr 15, 2010 #1
    Hi all,

    I am working on a programming project and want to know how many possible combinations can exist in a particular situation, but I have no idea how to work it out. It isn't homework, I just want to know because I am sure it is a VERY large number and want to make a point.

    There are 2 vectors, one vector is one dimensional and is, say, 5 in length with values in it: [ 1 | 2 | 3 | 4 | 5 ] and the second vector is two dimensional and empty (to be filled with the numbers in the one dimensional vector), say like so:
    +---------+
    | - | - | - |
    | - | - | - |
    | - | - | - |
    +---------+
    How would I go about working out working out how many combinations of those 5 numbers can be placed in the above two dimensional vector?
    eg. one would be:
    +---------+
    | 1 | 2 | 3 |
    | 4 | 5 | - |
    | - | - | - |
    +---------+
    another:
    +---------+
    | 1 | 3 | 2 |
    | 4 | 5 | - |
    | - | - | - |
    +---------+

    Thank you for any help :smile:
     
  2. jcsd
  3. Apr 15, 2010 #2
    There are 9 spots and 5 numbers to place in them. First pick 5 of the spots and then calculate the permutation of the 5 numbers in those 5 spots. I think this should be the answer, unless I am misunderstanding completely.

    [tex]\binom{9}{5} 5! = 15,120[/tex]

    This can also be calculated as the number of 5-permutations of 9 objects, since the first number would have 9 possible spots to occupy, the second would have 8 possibilities, etc...

    P(9,5) = 15,120
     
  4. Apr 15, 2010 #3
    Thanks for the quick reply! But what are permutations? I see that the 120 came from the 5! but I'm not sure what P(9,5) is... :confused:
     
  5. Apr 15, 2010 #4

    CRGreathouse

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    Science Advisor
    Homework Helper

    P(a, b) is the answer to your question with 9 slots in the matrix and 5 in the vector. It was defined on the spot, it's not a usual symbol.
     
  6. Apr 15, 2010 #5
    The intermediate step is P(9,5) = 9*8*7*6*5 = 15,120.

    Permutations are similar to combinations except in permutations, the order matters. In combinations, the order does not.
     
  7. Apr 16, 2010 #6
    Thank you very much for the help :smile:
     
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