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2x+y+z=15 , then number of positive integral solution.
if z=0 , y=15-2x >=1 1<=x<=7 , total solution 7if z=1 , y=14-2x >=1 1<=x<=6 , total solution 6if z =2, y=13-2x >=1 1<=x<=6 , total solution 6if z =3, y=12-2x >=1 1<=x<=5 , total solution 5if z =4, y=11-2x >=1 1<=x<= 5 , total solution 5if z =5, y=10-2x >=1 1<=x<= 4 , total solution 4if z =6, y= 9-2x >=1 1<=x<=4 , total solution 4if z =7, y=8-2x >=1 1<=x<=3 , total solution 3if z =8, y=7-2x >=1 1<=x<=3 , total solution 3if z =9, y=6-2x >=1 1<=x<=3 , total solution 2if z =10, y=5-2x >=1 1<=x<=3 , total solution 2if z =11, y=4-2x >=1 1<=x<=3 , total solution 1if z =12, y=3-2x >=1 1<=x<=3 , total solution 1if z =13, y=2-2x >=1 1<=x<=3 , total solution 0add all solutions , 7+2(6+4+3+2+1)=37sher mohammadB.Tech, IIT Delhi
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