Example: What is the number of integral solutions of the equation XITXTX 5 which satisfy0≤X1,0≤x2,1≤x3 Let x3=X3-1 x1+x2+x3=4, where0≤x1,0≤X2,0≤x f(y)=(1+y+y2+…)(1+y+y2+…)1+y+y2+…) =∑C(r+2,r)y 0▪ Example: What is the number of integral solutions of the equation ▪ x1+x2+x3=5 ▪ which satisfy 0x1 ,0x2 ,1x3? ▪ Let x3 '=x3 -1， ▪ x1+x2+x3 '=4, where 0x1 ,0x2 ,0x3 '   = = + − = = + + + + + + + + + 0 3 2 2 2 ( 2, ) (1 ) 1 ( ) (1 )(1 )(1 ) r r C r r y y f y y y  y y  y y 