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Math Help - 3's and 5's that equal 16

  1. #1
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    3's and 5's that equal 16

    Hi, I'm new here and very poor at math in general. I'm wondering, is there a simple formula of sorts for finding out how many combinations of two different numbers there are that equal another number? For example, how many combinations of 3's and 5's are there that equal 16? Such as, 3-5-3-5, 3-3-5-5, 3-5-5-3, 5-5-3-3 and 5-3-3-5. Thanks

    Mike
    Last edited by Codeseven; March 1st 2011 at 10:05 PM.
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  2. #2
    Senior Member Sambit's Avatar
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    For your example, two 3's and two 5's add up to 16. That is, total 4 numbers are here among which 2 are same and the rest 2 are also same.

    Note that, if there are N elements among which N_1 are of one type, N_2 are of another type,........,lastly N_k are of another type, where N_1+N_2+.......+N_k=N, then the total number of possible combinations is \frac{N!}{N_1! N_2! .... N_k!}. Compare this to you problem. What do you get then?
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  3. #3
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    Thanks Sambit. I gotta think about your reply, it might have gone over my head but I appreciate your help.

    Mike
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  4. #4
    Senior Member Sambit's Avatar
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    Further hint:- You have only N_1 and N_2, each equals 2, and N=N_1+N_2=4. Now think.
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