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at this point I saw more where did people live before the Industrial Revolution began

Total number of cases will be ::

x + y = z = 6 { x>=0 ,y>=0 ,z>=0 }

(6+3-1) C (3-1) =====

8 C =================28 2

hence the probaility of x=y=z=3 is 1/28

Since there are 28 options available and only one is favourable Therefore Probability = 1/28

If x(x+y) = y(y+z) = z(z+x) and x,y,z are positive integers. Then is it definitely true that x=y=z

If x, y, z are 3 non zero positive integers such that x+y+z = 8 and xy+yz+zx = 20, then What would be minimum possible value of x*y^2*z^2