"10 identical items..." - ??? What makes you think that they are identical?
Take a look at this:
number theory - Non-negative integral solutions of $X_1+X_2+X_3+X_4<n$ - Mathematics - Stack Exchange
Find the number of non-negative integer solutions of the inequality
x1 + x2 + x3 + x4 + x5 + x6 < 10.
Answer:
If this was -
Find the number of non-negative integer solutions of the equation
x1 + x2 + x3 + x4 + x5 + x6 = 10
I would view this as having 10 identical items to distribute among 6 people and would use .
However Im not sure how to handle it with when it's an equality. Would I write it as a summation formula?
"10 identical items..." - ??? What makes you think that they are identical?
Take a look at this:
number theory - Non-negative integral solutions of $X_1+X_2+X_3+X_4<n$ - Mathematics - Stack Exchange
They are identical in that they I am viewing this as having ten 'ones' that are being distributed among 6 people....
Taking x1 + x2 + x3 + x4 + x5 + x6 = 10
So x1 could have 5 'ones' and x2 - x6 could have one 'one' each. Which would be a solution for the equation.
Am I going about this the wrong way with that summation formula in my first post?