Is there a formula for this?
Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + x_9 + x_10 <= 2
in nonnegagive integers.
+1622 Yes there definitely is a good strategy. We have 10 different variables.
Case 1, the sum is = 0:
There is 1 solution, where all variables are equal to 0.
Case 2, the sum is = 1:
There are 10 choose 1 ways to arrange the value of 1 among the 10 variables, so there are 10 solutions.
Case 3, the sum is = 2.
We can have 10 ways to arrange the 2. But if we have two 1s, we have (10 choose 2) ways to do it = 45.
Total sum is 10 + 45 + 10 + 1 = 66 total cases.
