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# How many solutions do the equation have

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Hello,

I have a discrete math problem. It states how many solutions (X_1,...,X_6) in the Natural numbers have the equation X_1+ ... + X_6 = 10

So the way my teacher explained it was (10,0,0,0,0,0) would be one choice, (0,10,0,0,0,0) would be another, so basically it would look like this...

(10,0,0,0,0,0)
(0,10,0,0,0,0)
(0,0,10,0,0,0)
````````````````
(0,0,0,0,0,10)

THEN you have other solutions like
(1,9,0,0,0,0)
(0,1,9,0,0,0)
```````````````
(0,0,0,0,1,9)

And keep going until all the combinations of numbers are found.

I see that each, i suppose you would call them sets, have 6 combinations. So like (10) has 6, (1,9) has 6, ... you could do (1,1,8), or (1,1,1,7), or whatever else combinations. I just don't understand how to determine how many combinations there are.

Any help would be appreciated.

-John

https://brainmass.com/math/discrete-math/many-solutions-equation-have-447267

#### Solution Preview

How many solutions (X_1,...,X_6) have the equation X_1+ ... + X_6 = 10
Hello,

I have a discrete math problem. It states how many solutions (X_1,...,X_6) in the Natural numbers have the equation X_1+ ... + X_6 = 10

So the way my teacher explained it was (10,0,0,0,0,0) would be one choice, (0,10,0,0,0,0) would be another, so basically it would look like this...

Dear Student