SOLUTION: how many 6 number combinations are there in a 49 number field resulting in the total 275 the 49 number field is 1 --49

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Question 759808: how many 6 number combinations are there in a 49 number field resulting in the total 275 the 49 number field is 1 --49
Answer by Edwin McCravy(20081)   (Show Source): You can put this solution on YOUR website!
If we take the sum of the 6 largest nuumbers
in the field,

    44+45+46+47+48+49 = 279

That's 4 too large, so we must subtract
4 from both sides of that equation to 
have a sum of 275.  But all 6 must be 
different.

So we can do any of these: 

1.  subtract 1 each from the smallest 4
    numbers:

    44+45+46+47+48+49 = 279
    -1 -1 -1 -1          -4
    -----------------------
    43+44+45+46+48+49 = 275 


2.  subtract 2 each from the smallest two 
    numbers: 

    44+45+46+47+48+49 = 279
    -2 -2                -4
    -----------------------
    42+43+46+47+48+49 = 275
 
3.  subtract 2 from the smallest number, 
    and 1 each from the next smallest two: 

    44+45+46+47+48+49 = 279
    -2 -1 -1             -4
    -----------------------
    42+44+45+47+48+49 = 275

4.  subtract 3 from the smallest number, 
    and 1 from the next smallest number: 

    44+45+46+47+48+49 = 279
    -3 -1                -4
    -----------------------
    41+44+46+47+48+49 = 275

5.  subtract 4 from the smallest number: 

    44+45+46+47+48+49 = 279
    -4                   -4
    -----------------------
    40+45+46+47+48+49 = 275

That's 5 combinations.

Edwin
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