Diophantine
Probability
Level
4
Find the number of non-negative solutions of the equation above.
The answer is 74292.
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1 solution
Pretty long,
First of all we will sort out the variable with coefficient,
Let f = 0,1,2,3,4,5,6,7;
We have the following equations,
a+b+c+d+e = 28,24,20,16,12,8,4,0;
Now we to find no. of solutions of each and add them,
C(32,29) + C(28,24) + C(24,20) + C(20,16) + C(16,12) + C(12,8) + C(8,4) + C(4,0)
=74292