x+y+z =10
Number of way will be 10+3-1 C 3-1 = 66
Of all these 66 cases some are not valid
The conditions are x>=11, y>=6 , z>=4
Now x >=11 will be for 0 cases
Now y>=6 will be for x+y'+z = 10-6=4 so 4+3-1C 3-1= 15
Now z>=4 will be for x+y+z'= 10-4=6 so 6+3-1C3-1 = 28
But the conditions of y and z can be not valid when y=6 and z=4 is 1 way , this should be added as it will be subtracted for both y and z twice so the answer is 66-15-28+1= 24