11 th ball is yellow
So, 10 ball can select from green,11 th yellow=$_{10}^{10}\textrm{C}$+
9 " " " " " , 1 from yellow and 11 th yellow=$_{9}^{10}\textrm{C}\times_{1}^{9}\textrm{C}$ +
8 " " " " " 2 " " =$_{8}^{10}\textrm{C}\times_{2}^{9}\textrm{C}$ +
............................
2 " " " " 8 " " =$_{2}^{10}\textrm{C}\times_{8}^{9}\textrm{C}$
So, answer$_{10}^{10}\textrm{C}$+ $_{9}^{10}\textrm{C}\times_{1}^{9}\textrm{C}$ +$_{8}^{10}\textrm{C}\times_{2}^{9}\textrm{C}$ + ................. $_{2}^{10}\textrm{C}\times_{8}^{9}\textrm{C}$=45145